What is the derivative of f(x)=(1/(2x+3))^3 ?

The derivative of f(x)=(1/(2x+3))^3 is -6/((2x+3)^4)

What is the first derivative of f(x)=(1/(2x+3))^3 ?

The first derivative of f(x)=(1/(2x+3))^3 is -6/((2x+3)^4)

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derivative of

f (x) = (\frac{1}{2 x + 3})^{3}

- \frac{6}{( 2 x + 3 ) ^{4}}

Solution steps

\frac{d}{d x} ((\frac{1}{2 x + 3})^{3})

Apply the chain rule:

3 (\frac{1}{2 x + 3})^{2} \frac{d}{d x} (\frac{1}{2 x + 3})

= 3 (\frac{1}{2 x + 3})^{2} \frac{d}{d x} (\frac{1}{2 x + 3})

\frac{d}{d x} (\frac{1}{2 x + 3}) = - \frac{2}{( 2 x + 3 ) ^{2}}

= 3 (\frac{1}{2 x + 3})^{2} (- \frac{2}{( 2 x + 3 ) ^{2}})

Simplify

3 (\frac{1}{2 x + 3})^{2} (- \frac{2}{( 2 x + 3 ) ^{2}}) : - \frac{6}{( 2 x + 3 ) ^{4}}

= - \frac{6}{( 2 x + 3 ) ^{4}}

\frac{8}{x ^{2} + 4} (2.1)

\int \frac{1}{x ^{\frac{1}{5}} + 2} d x

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

f (x) = 4 x^{2}, at x = 9

What is the derivative of f(x)=(1/(2x+3))^3 ?
The derivative of f(x)=(1/(2x+3))^3 is -6/((2x+3)^4)
What is the first derivative of f(x)=(1/(2x+3))^3 ?
The first derivative of f(x)=(1/(2x+3))^3 is -6/((2x+3)^4)