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Popular >

derivative of 1/((2x+1^3))

Solution

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

Solution

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

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

= - \frac{3}{( 2 x + 1 ) ^{4}} \frac{d}{d x} (2 x + 1)

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

= - \frac{3}{( 2 x + 1 ) ^{4}} \cdot 2

Simplify

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

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

Popular Examples

integral of 1+t

\int 1 + t d t

derivative of ((x+30sqrt(x^2+100))/x)

\frac{d}{d x} (\frac{( x + 30 ) x ^{2} + 100}{x})

derivative of f(x)=sqrt(9+\sqrt{4x)}derivative of

f (x) = 9 + 4 x

integral of x^5+8x^3-9x^2+7x-5

\int x^{5} + 8 x^{3} - 9 x^{2} + 7 x - 5 d x

integral of-x^3+1/(x^2)

\int - x^{3} + \frac{1}{x ^{2}} d x

Frequently Asked Questions (FAQ)

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