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Ifg(x)=2loglogxxg\left(x\right)=\frac{2\log\log x}{x}g(x)=x2loglogx . Simplify derivative of quotient:
8xlnx+4x8x\ln x+4x8xlnx+4x
xx2\frac{x}{x^2}x2x
2xx2\frac{2x}{x^2}x22x
Iff(x)=x34xf\left(x\right)=\frac{x^3}{4x}f(x)=4xx3 .Simplify derivative of quotient:
2x
2x+2
x/2
Iff(x)=(2x−3)4x+2f\left(x\right)=\frac{\left(2x-3\right)}{4x+2}f(x)=4x+2(2x−3) .Simplify derivative of quotient:
4(2x+1)2\frac{4}{\left(2x+1\right)^2}(2x+1)24
8(x+1)2\frac{8}{\left(x+1\right)^2}(x+1)28
8(2x+1)2\frac{8}{\left(2x+1\right)^2}(2x+1)28
Simplify derivative of quotient:
f(x)=(2x−3)(2x+1)f\left(x\right)=\frac{\left(2x-3\right)}{\left(2x+1\right)}f(x)=(2x+1)(2x−3)
(3+x)(4−x)\frac{\left(3+x\right)}{\left(4-x\right)}(4−x)(3+x)
2(4−x)2\frac{2}{\left(4-x\right)^2}(4−x)22
Iff(x)=(x+2)2−xf\left(x\right)=\frac{\left(x+2\right)}{2-x}f(x)=2−x(x+2) .Simplify derivative of quotient:
2a(a−x)2\frac{2a}{\left(a-x\right)^2}(a−x)22a
2a(a+x)2\frac{2a}{\left(a+x\right)^2}(a+x)22a
4(2−x)2\frac{4}{\left(2-x\right)^2}(2−x)24
f(x)=(x2+1)(x2−3)f\left(x\right)=\frac{\left(x^2+1\right)}{\left(x^2-3\right)}f(x)=(x2−3)(x2+1)
−8x(x2−3)2-\frac{8x}{\left(x^2-3\right)^2}−(x2−3)28x
If f(x)=1+x1−xf\left(x\right)=\frac{\sqrt{1+x}}{\sqrt{1-x}}f(x)=1−x1+x . Simplify derivative of quotient:
5(1−x)(1−x2)\frac{5}{\left(1-x\right)\left(\sqrt{1-x^2}\right)}(1−x)(1−x2)5
1(1−x)(1−x2)\frac{1}{\left(1-x\right)\left(\sqrt{1-x^2}\right)}(1−x)(1−x2)1
2(1−x)(1−x2)\frac{2}{\left(1-x\right)\left(\sqrt{1-x^2}\right)}(1−x)(1−x2)2
f(x)=(4x−6)(2x+1)f\left(x\right)=\frac{\left(4x-6\right)}{\left(2x+1\right)}f(x)=(2x+1)(4x−6)
16(2x+1)2\frac{16}{\left(2x+1\right)^2}(2x+1)216
f(x)=(2+x)(2−x)f\left(x\right)=\frac{\left(2+x\right)}{\left(2-x\right)}f(x)=(2−x)(2+x)
8(4−x)2\frac{8}{\left(4-x\right)^2}(4−x)28
f(x)=(4+x)(4−x)f\left(x\right)=\frac{\left(4+x\right)}{\left(4-x\right)}f(x)=(4−x)(4+x)
It is done.