What is the derivative of-((64)/((1+4x)^3)) ?

The derivative of-((64)/((1+4x)^3)) is (768)/((1+4x)^4)

What is the first derivative of-((64)/((1+4x)^3)) ?

The first derivative of-((64)/((1+4x)^3)) is (768)/((1+4x)^4)

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derivative of

- (\frac{64}{( 1 + 4 x ) ^{3}})

\frac{768}{( 1 + 4 x ) ^{4}}

Solution steps

\frac{d}{d x} (- \frac{64}{( 1 + 4 x ) ^{3}})

Take the constant out:

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

= - 64 \frac{d}{d x} (\frac{1}{( 1 + 4 x ) ^{3}})

Apply exponent rule:

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

= - 64 \frac{d}{d x} ((1 + 4 x)^{- 3})

Apply the chain rule:

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

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

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

= - 64 (- \frac{3}{( 1 + 4 x ) ^{4}} \cdot 4)

Simplify

- 64 (- \frac{3}{( 1 + 4 x ) ^{4}} \cdot 4) : \frac{768}{( 1 + 4 x ) ^{4}}

= \frac{768}{( 1 + 4 x ) ^{4}}

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y^{^{'}} + y - 2 sin (x) = 0

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What is the derivative of-((64)/((1+4x)^3)) ?
The derivative of-((64)/((1+4x)^3)) is (768)/((1+4x)^4)
What is the first derivative of-((64)/((1+4x)^3)) ?
The first derivative of-((64)/((1+4x)^3)) is (768)/((1+4x)^4)