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Higher-Order Differentiation

Fill in the blank:
If $f\left(x\right)=\sin3x$ . $f^{\left(4\right)}\left(x\right)=$ __________.

$81x$

$-60\cos x+81x$

Find the third derivative of the function $y=3x^3$ .

$6x^2$

$18x$

$18$

Fill in the blank:
If $f\left(x\right)=x^9+22x$ . Then find $f^{\left(8\right)}\left(x\right)$ .

$362880x$

$362880$

$362880x$

Fill in the blank:
If $f\left(x\right)=x^7-3x^4$ . Then find $f^{\left(8\right)}\left(x\right)$ .

0

8

81

If $f\left(x\right)=4x^2+1$ , then find $4th$ order derivative of $f\left(x\right)$ .

4

3

0

What is the notation for 11th order derivative of $f\left(x\right)$ ?

$f\left(11x\right)$

$f^{\left(11\right)}\left(x\right)$

$f^{11}\left(x\right)$

Fill in the blank:
If $f\left(x\right)=\tan3x$ . Then find $4th$ order derivative of $f\left(x\right)$ .

$18\left(363x\ 2x+723x\ \tan3x\right)$

$32\left(363x\ 2x+723x\ \tan3x\right)$

$8\left(63x\ 2x+723x\ \tan3x\right)$

Find the third derivative of the function $y=\ln\ln x^9$ .

$-\frac{1}{x^3}$

$\frac{8}{x^3}$

$\frac{18}{x^3}$

Fill in the blank:
If $f\left(x\right)=x^7-3x^4+x$ . $f^{\left(4\right)}\left(x\right)=$ __________.

$12x^7-72$

$840x^3-72$

$120x-72$

What is the notation for 5th order derivative of f(x)?

$f\left(5x\right)$

$f^{\left(5\right)}\left(x\right)$

$f^5\left(x\right)$

Questions

Time

Score

Higher-Order Differentiation

Fill in the blank:If ﻿f(x)=sin⁡3xf\left(x\right)=\sin3xf(x)=sin3x﻿. ﻿f(4)(x)=f^{\left(4\right)}\left(x\right)=f(4)(x)=﻿ __________.

﻿81x81x81x﻿

﻿81x81x81x﻿

﻿−60cos⁡x+81x-60\cos x+81x−60cosx+81x﻿

Find the third derivative of the function ﻿y=3x3y=3x^3y=3x3﻿.

﻿6x26x^26x2﻿

﻿18x18x18x﻿

﻿181818﻿

Fill in the blank:If ﻿f(x)=x9+22xf\left(x\right)=x^9+22xf(x)=x9+22x﻿. Then find ﻿f(8)(x)f^{\left(8\right)}\left(x\right)f(8)(x)﻿.

﻿362880x362880x362880x﻿

﻿362880362880362880﻿

﻿362880x362880x362880x﻿

Fill in the blank:If ﻿f(x)=x7−3x4f\left(x\right)=x^7-3x^4f(x)=x7−3x4﻿. Then find ﻿f(8)(x)f^{\left(8\right)}\left(x\right)f(8)(x)﻿.

0

8

81

If ﻿f(x)=4x2+1f\left(x\right)=4x^2+1f(x)=4x2+1﻿, then find ﻿4th4th4th﻿ order derivative of ﻿f(x)f\left(x\right)f(x)﻿.

4

3

0

What is the notation for 11th order derivative of ﻿f(x)f\left(x\right)f(x)﻿?

﻿f(11x)f\left(11x\right)f(11x)﻿

﻿f(11)(x)f^{\left(11\right)}\left(x\right)f(11)(x)﻿

﻿f11(x)f^{11}\left(x\right)f11(x)﻿

Fill in the blank:If ﻿f(x)=tan⁡3xf\left(x\right)=\tan3xf(x)=tan3x﻿. Then find ﻿4th4th4th﻿ order derivative of ﻿f(x)f\left(x\right)f(x)﻿.

﻿18(363x 2x+723x tan⁡3x)18\left(363x\ 2x+723x\ \tan3x\right)18(363x 2x+723x tan3x)﻿

﻿32(363x 2x+723x tan⁡3x)32\left(363x\ 2x+723x\ \tan3x\right)32(363x 2x+723x tan3x)﻿

﻿8(63x 2x+723x tan⁡3x)8\left(63x\ 2x+723x\ \tan3x\right)8(63x 2x+723x tan3x)﻿

Find the third derivative of the function ﻿y=ln⁡ln⁡x9y=\ln\ln x^9y=lnlnx9﻿.

﻿−1x3-\frac{1}{x^3}−x31​﻿

﻿8x3\frac{8}{x^3}x38​﻿

﻿18x3\frac{18}{x^3}x318​﻿

Fill in the blank:If ﻿f(x)=x7−3x4+xf\left(x\right)=x^7-3x^4+xf(x)=x7−3x4+x﻿. ﻿f(4)(x)=f^{\left(4\right)}\left(x\right)=f(4)(x)=﻿ __________.

﻿12x7−7212x^7-7212x7−72﻿

﻿840x3−72840x^3-72840x3−72﻿

﻿120x−72120x-72120x−72﻿

What is the notation for 5th order derivative of f(x)?

﻿f(5x)f\left(5x\right)f(5x)﻿

﻿f(5)(x)f^{\left(5\right)}\left(x\right)f(5)(x)﻿

﻿f5(x)f^5\left(x\right)f5(x)﻿

Incorrect

Great!

Fill in the blank:
If $f\left(x\right)=\sin3x$ . $f^{\left(4\right)}\left(x\right)=$ __________.

$81x$

$81x$

$-60\cos x+81x$

Find the third derivative of the function $y=3x^3$ .

$6x^2$

$18x$

$18$

Fill in the blank:
If $f\left(x\right)=x^9+22x$ . Then find $f^{\left(8\right)}\left(x\right)$ .

$362880x$

$362880$

$362880x$

Fill in the blank:
If $f\left(x\right)=x^7-3x^4$ . Then find $f^{\left(8\right)}\left(x\right)$ .

If $f\left(x\right)=4x^2+1$ , then find $4th$ order derivative of $f\left(x\right)$ .

What is the notation for 11th order derivative of $f\left(x\right)$ ?

$f\left(11x\right)$

$f^{\left(11\right)}\left(x\right)$

$f^{11}\left(x\right)$

Fill in the blank:
If $f\left(x\right)=\tan3x$ . Then find $4th$ order derivative of $f\left(x\right)$ .

$18\left(363x\ 2x+723x\ \tan3x\right)$

$32\left(363x\ 2x+723x\ \tan3x\right)$

$8\left(63x\ 2x+723x\ \tan3x\right)$

Find the third derivative of the function $y=\ln\ln x^9$ .

$-\frac{1}{x^3}$

$\frac{8}{x^3}$

$\frac{18}{x^3}$

Fill in the blank:
If $f\left(x\right)=x^7-3x^4+x$ . $f^{\left(4\right)}\left(x\right)=$ __________.

$12x^7-72$

$840x^3-72$

$120x-72$

$f\left(5x\right)$

$f^{\left(5\right)}\left(x\right)$

$f^5\left(x\right)$