What is the derivative of sqrt(x)(1-5sqrt(x)) ?

The derivative of sqrt(x)(1-5sqrt(x)) is (1-5sqrt(x))/(2sqrt(x))-5/2

What is the first derivative of sqrt(x)(1-5sqrt(x)) ?

The first derivative of sqrt(x)(1-5sqrt(x)) is (1-5sqrt(x))/(2sqrt(x))-5/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

x (1 - 5 x)

\frac{1 - 5 x}{2 x} - \frac{5}{2}

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = 1 - 5 x

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

\frac{d}{d x} (x) = \frac{1}{2 x}

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

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

Simplify

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

= \frac{1 - 5 x}{2 x} - \frac{5}{2}

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