What is the derivative of f(x)=((x-4)/(x+4))^4 ?

The derivative of f(x)=((x-4)/(x+4))^4 is (32(x-4)^3)/((x+4)^5)

What is the first derivative of f(x)=((x-4)/(x+4))^4 ?

The first derivative of f(x)=((x-4)/(x+4))^4 is (32(x-4)^3)/((x+4)^5)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

f (x) = (\frac{x - 4}{x + 4})^{4}

\frac{32 ( x - 4 ) ^{3}}{( x + 4 ) ^{5}}

Solution steps

\frac{d}{d x} ((\frac{x - 4}{x + 4})^{4})

Apply the chain rule:

4 (\frac{x - 4}{x + 4})^{3} \frac{d}{d x} (\frac{x - 4}{x + 4})

= 4 (\frac{x - 4}{x + 4})^{3} \frac{d}{d x} (\frac{x - 4}{x + 4})

\frac{d}{d x} (\frac{x - 4}{x + 4}) = \frac{8}{( x + 4 ) ^{2}}

= 4 (\frac{x - 4}{x + 4})^{3} \frac{8}{( x + 4 ) ^{2}}

Simplify

4 (\frac{x - 4}{x + 4})^{3} \frac{8}{( x + 4 ) ^{2}} : \frac{32 ( x - 4 ) ^{3}}{( x + 4 ) ^{5}}

= \frac{32 ( x - 4 ) ^{3}}{( x + 4 ) ^{5}}

\int_{0}^{1} \frac{1}{1 + sin ( 2 x )} d x

\int \frac{( x + 6 )}{( x + 7 )} d x

\frac{d}{d y} (2 x - y)

\frac{d}{d x} (\frac{ln ( x ^{2} )}{x ^{2}})

\int \frac{1}{9 - 2 x} d x

What is the derivative of f(x)=((x-4)/(x+4))^4 ?
The derivative of f(x)=((x-4)/(x+4))^4 is (32(x-4)^3)/((x+4)^5)
What is the first derivative of f(x)=((x-4)/(x+4))^4 ?
The first derivative of f(x)=((x-4)/(x+4))^4 is (32(x-4)^3)/((x+4)^5)