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

The derivative of 1/((x^3+sin(x))^2) is -(2(3x^2+cos(x)))/((x^3+sin(x))^3)

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

The first derivative of 1/((x^3+sin(x))^2) is -(2(3x^2+cos(x)))/((x^3+sin(x))^3)

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derivative of

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

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