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Simplify Derivatives By Factoring Out The Least Powers

Simplify by factoring out the least powers
f’(x) = (1-x²)^1/2 + (1-x²)^-1/2

$\frac{\left|2x-3x^3\right|}{\sqrt{1-x^2}}$

$\frac{\left|2-x^2\right|}{\sqrt{1-x^2}}$

$\frac{\left|1-2x^2\right|}{\sqrt{1-x^2}}$

Simplify by factoring out the least powers
f’(x) = (1/5) x^-1/2 – (3/5) (x)^1/2

$\frac{1}{5}\left(\frac{1}{\sqrt{x}}-3\sqrt{x}\right)$

$\frac{1}{2}\left(\frac{1}{\sqrt{x}}-3\sqrt{x}\right)$

$-3\left(\frac{1}{x^4}+\frac{1}{x^{\frac{5}{2}}}\right)$

Simplify by factoring out the least powers
f’(x) = x^-4+ x^-3/2

$\frac{\left|-x^2\right|}{\sqrt{1-x^2}}$

$2\left(\frac{1}{x^4}+\frac{1}{x^{\frac{3}{2}}}\right)$

$-3\left(\frac{1}{x^4}+\frac{1}{x^{\frac{5}{2}}}\right)$

Simplify by factoring out the least powers
f’(x) = 2 x^-4 + 2(x)^-3/2

$\frac{\left|-x^2\right|}{\sqrt{1-x^2}}$

$2\left(\frac{1}{x^4}+\frac{1}{x^{\frac{3}{2}}}\right)$

$-3\left(\frac{1}{x^4}+\frac{1}{x^{\frac{3}{2}}}\right)$

Simplify by factoring out the least powers
f’(x) = (1-x² )^1/2 – x² (1- x²)^-1/2

$\frac{\left|2x-3x^3\right|}{\sqrt{1-x^2}}$

$\frac{\left|x+3x^3\right|}{\sqrt{1-x^2}}$

$\frac{\left|1-2x^2\right|}{\sqrt{1-x^2}}$

Simplify by factoring out the least powers
f’(x) = (1-x² )^1/2 –(1- x²)^-1/2

$\frac{\left|2x-3x^3\right|}{\sqrt{1-x^2}}$

$\frac{\left|-x^2\right|}{\sqrt{1-x^2}}$

$\frac{\left|1-2x^2\right|}{\sqrt{1-x^2}}$

Simplify by factoring out the least powers
f’(x) = 5x^-4+ 5x^-1/2-5

$5\left(\frac{1}{x^4}+\frac{1}{x^{\frac{1}{2}}}-1\right)$

$\frac{\left[-x^2\right]}{\sqrt{1-x^2}}$

$-3\left(\frac{1}{x^4}+\frac{1}{x^{\frac{5}{2}}}\right)$

Simplify by factoring out the least powers
f’(x) =(1/7) x^-1/2-(3/7)x^1/2

$\frac{1}{7}\left(\frac{1}{\sqrt{x}}-3\sqrt{x}\right)$

$\frac{1}{2}\left(\frac{1}{\sqrt{x}}-3\sqrt{x}\right)$

$-3\left(\frac{1}{x^4}+\frac{1}{x^{\frac{5}{2}}}\right)$

Simplify by factoring out the least powers
f’(x) = -3x^-4 -3 x^-5/2+3

$\frac{\left|2x-3x^3\right|}{\sqrt{1-x^2}}$

$-3\left(\frac{1}{x^4}+\frac{1}{x^{\frac{5}{2}}}+1\right)$

$-3\left(\frac{1}{x^4}+\frac{1}{x^{\frac{5}{2}}}\right)$

Simplify by factoring out the least powers
f’(x) = (1/2) x^-1/2 – (3/2) (x)^1/2

$\frac{\left|-x^2\right|}{\sqrt{1-x^2}}$

$\frac{1}{2}\left(\frac{1}{\sqrt{x}}-3\sqrt{x}\right)$

$-3\left(\frac{1}{x^4}+\frac{1}{x^{\frac{5}{2}}}\right)$

Questions

Time

Score

Simplify Derivatives By Factoring Out The Least Powers

Simplify by factoring out the least powersf’(x) = (1-x2)1/2 + (1-x2)-1/2

﻿∣2x−3x3∣1−x2\frac{\left|2x-3x^3\right|}{\sqrt{1-x^2}}1−x2​∣2x−3x3∣​﻿

﻿∣2−x2∣1−x2\frac{\left|2-x^2\right|}{\sqrt{1-x^2}}1−x2​∣2−x2∣​﻿

﻿∣1−2x2∣1−x2\frac{\left|1-2x^2\right|}{\sqrt{1-x^2}}1−x2​∣1−2x2∣​﻿

Simplify by factoring out the least powersf’(x) = (1/5) x-1/2 – (3/5) (x)1/2

﻿15(1x−3x)\frac{1}{5}\left(\frac{1}{\sqrt{x}}-3\sqrt{x}\right)51​(x​1​−3x​)﻿

﻿12(1x−3x)\frac{1}{2}\left(\frac{1}{\sqrt{x}}-3\sqrt{x}\right)21​(x​1​−3x​)﻿

﻿−3(1x4+1x52)-3\left(\frac{1}{x^4}+\frac{1}{x^{\frac{5}{2}}}\right)−3(x41​+x25​1​)﻿

Simplify by factoring out the least powersf’(x) = x-4+ x-3/2

﻿∣−x2∣1−x2\frac{\left|-x^2\right|}{\sqrt{1-x^2}}1−x2​∣−x2∣​﻿

﻿2(1x4+1x32)2\left(\frac{1}{x^4}+\frac{1}{x^{\frac{3}{2}}}\right)2(x41​+x23​1​)﻿

﻿−3(1x4+1x52)-3\left(\frac{1}{x^4}+\frac{1}{x^{\frac{5}{2}}}\right)−3(x41​+x25​1​)﻿

Simplify by factoring out the least powersf’(x) = 2 x-4 + 2(x)-3/2

﻿∣−x2∣1−x2\frac{\left|-x^2\right|}{\sqrt{1-x^2}}1−x2​∣−x2∣​﻿

﻿2(1x4+1x32)2\left(\frac{1}{x^4}+\frac{1}{x^{\frac{3}{2}}}\right)2(x41​+x23​1​)﻿

﻿−3(1x4+1x32)-3\left(\frac{1}{x^4}+\frac{1}{x^{\frac{3}{2}}}\right)−3(x41​+x23​1​)﻿

Simplify by factoring out the least powersf’(x) = (1-x2 )1/2 – x2 (1- x2)-1/2

﻿∣2x−3x3∣1−x2\frac{\left|2x-3x^3\right|}{\sqrt{1-x^2}}1−x2​∣2x−3x3∣​﻿

﻿∣x+3x3∣1−x2\frac{\left|x+3x^3\right|}{\sqrt{1-x^2}}1−x2​∣x+3x3∣​﻿

﻿∣1−2x2∣1−x2\frac{\left|1-2x^2\right|}{\sqrt{1-x^2}}1−x2​∣1−2x2∣​﻿

Simplify by factoring out the least powersf’(x) = (1-x2 )1/2 –(1- x2)-1/2

﻿∣2x−3x3∣1−x2\frac{\left|2x-3x^3\right|}{\sqrt{1-x^2}}1−x2​∣2x−3x3∣​﻿

﻿∣−x2∣1−x2\frac{\left|-x^2\right|}{\sqrt{1-x^2}}1−x2​∣−x2∣​﻿

﻿∣1−2x2∣1−x2\frac{\left|1-2x^2\right|}{\sqrt{1-x^2}}1−x2​∣1−2x2∣​﻿

Simplify by factoring out the least powersf’(x) = 5x-4+ 5x-1/2-5

﻿5(1x4+1x12−1)5\left(\frac{1}{x^4}+\frac{1}{x^{\frac{1}{2}}}-1\right)5(x41​+x21​1​−1)﻿

﻿[−x2]1−x2\frac{\left[-x^2\right]}{\sqrt{1-x^2}}1−x2​[−x2]​﻿

﻿−3(1x4+1x52)-3\left(\frac{1}{x^4}+\frac{1}{x^{\frac{5}{2}}}\right)−3(x41​+x25​1​)﻿

Simplify by factoring out the least powersf’(x) =(1/7) x-1/2-(3/7)x1/2

﻿17(1x−3x)\frac{1}{7}\left(\frac{1}{\sqrt{x}}-3\sqrt{x}\right)71​(x​1​−3x​)﻿

﻿12(1x−3x)\frac{1}{2}\left(\frac{1}{\sqrt{x}}-3\sqrt{x}\right)21​(x​1​−3x​)﻿

﻿−3(1x4+1x52)-3\left(\frac{1}{x^4}+\frac{1}{x^{\frac{5}{2}}}\right)−3(x41​+x25​1​)﻿

Simplify by factoring out the least powersf’(x) = -3x-4 -3 x-5/2+3

﻿∣2x−3x3∣1−x2\frac{\left|2x-3x^3\right|}{\sqrt{1-x^2}}1−x2​∣2x−3x3∣​﻿

﻿−3(1x4+1x52+1)-3\left(\frac{1}{x^4}+\frac{1}{x^{\frac{5}{2}}}+1\right)−3(x41​+x25​1​+1)﻿

﻿−3(1x4+1x52)-3\left(\frac{1}{x^4}+\frac{1}{x^{\frac{5}{2}}}\right)−3(x41​+x25​1​)﻿

Simplify by factoring out the least powersf’(x) = (1/2) x-1/2 – (3/2) (x)1/2

﻿∣−x2∣1−x2\frac{\left|-x^2\right|}{\sqrt{1-x^2}}1−x2​∣−x2∣​﻿

﻿12(1x−3x)\frac{1}{2}\left(\frac{1}{\sqrt{x}}-3\sqrt{x}\right)21​(x​1​−3x​)﻿

﻿−3(1x4+1x52)-3\left(\frac{1}{x^4}+\frac{1}{x^{\frac{5}{2}}}\right)−3(x41​+x25​1​)﻿

Incorrect

Great!

Simplify by factoring out the least powers
f’(x) = (1-x²)^1/2 + (1-x²)^-1/2

$\frac{\left|2x-3x^3\right|}{\sqrt{1-x^2}}$

$\frac{\left|2-x^2\right|}{\sqrt{1-x^2}}$

$\frac{\left|1-2x^2\right|}{\sqrt{1-x^2}}$

Simplify by factoring out the least powers
f’(x) = (1/5) x^-1/2 – (3/5) (x)^1/2

$\frac{1}{5}\left(\frac{1}{\sqrt{x}}-3\sqrt{x}\right)$

$\frac{1}{2}\left(\frac{1}{\sqrt{x}}-3\sqrt{x}\right)$

$-3\left(\frac{1}{x^4}+\frac{1}{x^{\frac{5}{2}}}\right)$

Simplify by factoring out the least powers
f’(x) = x^-4+ x^-3/2

$\frac{\left|-x^2\right|}{\sqrt{1-x^2}}$

$2\left(\frac{1}{x^4}+\frac{1}{x^{\frac{3}{2}}}\right)$

$-3\left(\frac{1}{x^4}+\frac{1}{x^{\frac{5}{2}}}\right)$

Simplify by factoring out the least powers
f’(x) = 2 x^-4 + 2(x)^-3/2

$\frac{\left|-x^2\right|}{\sqrt{1-x^2}}$

$2\left(\frac{1}{x^4}+\frac{1}{x^{\frac{3}{2}}}\right)$

$-3\left(\frac{1}{x^4}+\frac{1}{x^{\frac{3}{2}}}\right)$

Simplify by factoring out the least powers
f’(x) = (1-x² )^1/2 – x² (1- x²)^-1/2

$\frac{\left|2x-3x^3\right|}{\sqrt{1-x^2}}$

$\frac{\left|x+3x^3\right|}{\sqrt{1-x^2}}$

$\frac{\left|1-2x^2\right|}{\sqrt{1-x^2}}$

Simplify by factoring out the least powers
f’(x) = (1-x² )^1/2 –(1- x²)^-1/2

$\frac{\left|2x-3x^3\right|}{\sqrt{1-x^2}}$

$\frac{\left|-x^2\right|}{\sqrt{1-x^2}}$

$\frac{\left|1-2x^2\right|}{\sqrt{1-x^2}}$

Simplify by factoring out the least powers
f’(x) = 5x^-4+ 5x^-1/2-5

$5\left(\frac{1}{x^4}+\frac{1}{x^{\frac{1}{2}}}-1\right)$

$\frac{\left[-x^2\right]}{\sqrt{1-x^2}}$

$-3\left(\frac{1}{x^4}+\frac{1}{x^{\frac{5}{2}}}\right)$

Simplify by factoring out the least powers
f’(x) =(1/7) x^-1/2-(3/7)x^1/2

$\frac{1}{7}\left(\frac{1}{\sqrt{x}}-3\sqrt{x}\right)$

$\frac{1}{2}\left(\frac{1}{\sqrt{x}}-3\sqrt{x}\right)$

$-3\left(\frac{1}{x^4}+\frac{1}{x^{\frac{5}{2}}}\right)$

Simplify by factoring out the least powers
f’(x) = -3x^-4 -3 x^-5/2+3

$\frac{\left|2x-3x^3\right|}{\sqrt{1-x^2}}$

$-3\left(\frac{1}{x^4}+\frac{1}{x^{\frac{5}{2}}}+1\right)$

$-3\left(\frac{1}{x^4}+\frac{1}{x^{\frac{5}{2}}}\right)$

Simplify by factoring out the least powers
f’(x) = (1/2) x^-1/2 – (3/2) (x)^1/2

$\frac{\left|-x^2\right|}{\sqrt{1-x^2}}$

$\frac{1}{2}\left(\frac{1}{\sqrt{x}}-3\sqrt{x}\right)$

$-3\left(\frac{1}{x^4}+\frac{1}{x^{\frac{5}{2}}}\right)$