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

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

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

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

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\frac{d}{d 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 exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

y = x^{2} ln (7 x)

a \to \infty lim (a^{2})

\int_{1}^{6} \frac{6}{x} d x

\frac{d}{d x} (\frac{e ^{s i n (x)}}{2 + cos ( π ) x})

\frac{d y}{d x}, y^{4} = x^{5}

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