What is the derivative of 4/((x+4^2)) ?

The derivative of 4/((x+4^2)) is -8/((x+4)^3)

What is the first derivative of 4/((x+4^2)) ?

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

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

- \frac{8}{( x + 4 ) ^{3}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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