What is the derivative of f(x)=(14)/((x+4)^3) ?

The derivative of f(x)=(14)/((x+4)^3) is -(42)/((x+4)^4)

What is the first derivative of f(x)=(14)/((x+4)^3) ?

The first derivative of f(x)=(14)/((x+4)^3) is -(42)/((x+4)^4)

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derivative of

f (x) = \frac{14}{( x + 4 ) ^{3}}

- \frac{42}{( x + 4 ) ^{4}}

Solution steps

\frac{d}{d x} (\frac{14}{( x + 4 ) ^{3}})

Take the constant out:

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

= 14 \frac{d}{d x} (\frac{1}{( x + 4 ) ^{3}})

Apply exponent rule:

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

= 14 \frac{d}{d x} ((x + 4)^{- 3})

Apply the chain rule:

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

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

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

= 14 (- \frac{3}{( x + 4 ) ^{4}} \cdot 1)

Simplify

14 (- \frac{3}{( x + 4 ) ^{4}} \cdot 1) : - \frac{42}{( x + 4 ) ^{4}}

= - \frac{42}{( x + 4 ) ^{4}}

\frac{d y}{d x} = \frac{cos ( x )}{y}

n = 1 \sum \infty \frac{5 n}{2 n - 1}

\int t k d t

\int_{0}^{1} x - 1 d x

\frac{8}{x}

What is the derivative of f(x)=(14)/((x+4)^3) ?
The derivative of f(x)=(14)/((x+4)^3) is -(42)/((x+4)^4)
What is the first derivative of f(x)=(14)/((x+4)^3) ?
The first derivative of f(x)=(14)/((x+4)^3) is -(42)/((x+4)^4)