What is the derivative of f(x)=-8/((1+4x)^2) ?

The derivative of f(x)=-8/((1+4x)^2) is (64)/((1+4x)^3)

What is the first derivative of f(x)=-8/((1+4x)^2) ?

The first derivative of f(x)=-8/((1+4x)^2) is (64)/((1+4x)^3)

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derivative of

f (x) = - \frac{8}{( 1 + 4 x ) ^{2}}

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

Solution steps

\frac{d}{d x} (- \frac{8}{( 1 + 4 x ) ^{2}})

Take the constant out:

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

= - 8 \frac{d}{d x} (\frac{1}{( 1 + 4 x ) ^{2}})

Apply exponent rule:

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

= - 8 \frac{d}{d x} ((1 + 4 x)^{- 2})

Apply the chain rule:

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

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

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

= - 8 (- \frac{2}{( 1 + 4 x ) ^{3}} \cdot 4)

Simplify

- 8 (- \frac{2}{( 1 + 4 x ) ^{3}} \cdot 4) : \frac{64}{( 1 + 4 x ) ^{3}}

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

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What is the derivative of f(x)=-8/((1+4x)^2) ?
The derivative of f(x)=-8/((1+4x)^2) is (64)/((1+4x)^3)
What is the first derivative of f(x)=-8/((1+4x)^2) ?
The first derivative of f(x)=-8/((1+4x)^2) is (64)/((1+4x)^3)