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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

integral of sin^2(x+2)

\int sin^{2} (x + 2) d x

derivative of (-2/(\sqrt[3]{x)})

integral of sqrt(144-t^2)

\int 144 - t^{2} d t

integral from 0 to 5 of (2e^x+4cos(x))

\int_{0}^{5} (2 e^{x} + 4 cos (x)) d x

limit as x approaches 2-of (3x)/(x^2-4)

x \to 2 - lim (\frac{3 x}{x ^{2} - 4})

Frequently Asked Questions (FAQ)

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