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

The derivative of 5/(1+5x) is -(25)/((1+5x)^2)

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

The first derivative of 5/(1+5x) is -(25)/((1+5x)^2)

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{5}{1 + 5 x})

- \frac{25}{( 1 + 5 x ) ^{2}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

= - \frac{1}{( 1 + 5 x ) ^{2}} \frac{d}{d x} (1 + 5 x)

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

= 5 (- \frac{1}{( 1 + 5 x ) ^{2}} \cdot 5)

Simplify

5 (- \frac{1}{( 1 + 5 x ) ^{2}} \cdot 5) : - \frac{25}{( 1 + 5 x ) ^{2}}

= - \frac{25}{( 1 + 5 x ) ^{2}}

n \to \infty lim (3 + \frac{1}{n})

\int 2 cos^{4} (x) d x

\int 9 - 4 x - 4 x^{2} d x

\int_{0}^{2} 7 e^{- 3 x} d x

\frac{d}{d x} (cos^{2} (5 x))

What is the derivative of 5/(1+5x) ?
The derivative of 5/(1+5x) is -(25)/((1+5x)^2)
What is the first derivative of 5/(1+5x) ?
The first derivative of 5/(1+5x) is -(25)/((1+5x)^2)