What is the derivative of f(x)=(168)/((x+4)^5) ?

The derivative of f(x)=(168)/((x+4)^5) is -(840)/((x+4)^6)

What is the first derivative of f(x)=(168)/((x+4)^5) ?

The first derivative of f(x)=(168)/((x+4)^5) is -(840)/((x+4)^6)

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derivative of

f (x) = \frac{168}{( x + 4 ) ^{5}}

- \frac{840}{( x + 4 ) ^{6}}

Solution steps

\frac{d}{d x} (\frac{168}{( x + 4 ) ^{5}})

Take the constant out:

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

= 168 \frac{d}{d x} (\frac{1}{( x + 4 ) ^{5}})

Apply exponent rule:

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

= 168 \frac{d}{d x} ((x + 4)^{- 5})

Apply the chain rule:

- \frac{5}{( x + 4 ) ^{6}} \frac{d}{d x} (x + 4)

= - \frac{5}{( x + 4 ) ^{6}} \frac{d}{d x} (x + 4)

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

= 168 (- \frac{5}{( x + 4 ) ^{6}} \cdot 1)

Simplify

168 (- \frac{5}{( x + 4 ) ^{6}} \cdot 1) : - \frac{840}{( x + 4 ) ^{6}}

= - \frac{840}{( x + 4 ) ^{6}}

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What is the derivative of f(x)=(168)/((x+4)^5) ?
The derivative of f(x)=(168)/((x+4)^5) is -(840)/((x+4)^6)
What is the first derivative of f(x)=(168)/((x+4)^5) ?
The first derivative of f(x)=(168)/((x+4)^5) is -(840)/((x+4)^6)