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

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

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

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

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int \frac{2 x}{cos ^{2} ( 2 x )} d x

f (x) = - x^{2}

y^{^{'}} - 6 y = 5

\int \frac{5 x - 7}{( x ^{2} - x - 2 ) ( x - 3 )} d x

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