What is the derivative of f(x)=(100)/((1+5x)^3) ?

The derivative of f(x)=(100)/((1+5x)^3) is -(1500)/((1+5x)^4)

What is the first derivative of f(x)=(100)/((1+5x)^3) ?

The first derivative of f(x)=(100)/((1+5x)^3) is -(1500)/((1+5x)^4)

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derivative of

f (x) = \frac{100}{( 1 + 5 x ) ^{3}}

- \frac{1500}{( 1 + 5 x ) ^{4}}

Solution steps

\frac{d}{d x} (\frac{100}{( 1 + 5 x ) ^{3}})

Take the constant out:

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

= 100 \frac{d}{d x} (\frac{1}{( 1 + 5 x ) ^{3}})

Apply exponent rule:

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

= 100 \frac{d}{d x} ((1 + 5 x)^{- 3})

Apply the chain rule:

- \frac{3}{( 1 + 5 x ) ^{4}} \frac{d}{d x} (1 + 5 x)

= - \frac{3}{( 1 + 5 x ) ^{4}} \frac{d}{d x} (1 + 5 x)

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

= 100 (- \frac{3}{( 1 + 5 x ) ^{4}} \cdot 5)

Simplify

100 (- \frac{3}{( 1 + 5 x ) ^{4}} \cdot 5) : - \frac{1500}{( 1 + 5 x ) ^{4}}

= - \frac{1500}{( 1 + 5 x ) ^{4}}

\int x^{3} + sin (x) + cos (x) d x

\int e^{8 x} sin (9 x) d x

f (x) = tan^{2} (3 e^{x})

\frac{7}{( 2 x + 1 ) ^{2}}

x^{^{''}} = - x + 0.1 x^{^{'}}

What is the derivative of f(x)=(100)/((1+5x)^3) ?
The derivative of f(x)=(100)/((1+5x)^3) is -(1500)/((1+5x)^4)
What is the first derivative of f(x)=(100)/((1+5x)^3) ?
The first derivative of f(x)=(100)/((1+5x)^3) is -(1500)/((1+5x)^4)