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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d 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 \frac{1 + tan ( x )}{1 - tan ( x )} d x

x \to \infty lim ((1 - \frac{1}{4 x})^{8 x})

\int \frac{1}{x ^{2} e ^{\frac{1}{x}}} d x

\int (5 x - 1) (3 x^{2} + 2) d x

\int e^{x^{3}} (12 x^{2}) d x

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