What is the derivative of x(2x-5^3) ?

The derivative of x(2x-5^3) is (2x-5)^3+6x(2x-5)^2

What is the first derivative of x(2x-5^3) ?

The first derivative of x(2x-5^3) is (2x-5)^3+6x(2x-5)^2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (x (2 x - 5)^{3})

(2 x - 5)^{3} + 6 x (2 x - 5)^{2}

Solution steps

\frac{d}{d x} (x (2 x - 5)^{3})

Apply the Product Rule:

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

f = x, g = (2 x - 5)^{3}

= \frac{d x}{d x} (2 x - 5)^{3} + \frac{d}{d x} ((2 x - 5)^{3}) x

\frac{d x}{d x} = 1

\frac{d}{d x} ((2 x - 5)^{3}) = 6 (2 x - 5)^{2}

= 1 \cdot (2 x - 5)^{3} + 6 (2 x - 5)^{2} x

Simplify

= (2 x - 5)^{3} + 6 x (2 x - 5)^{2}

What is the derivative of x(2x-5^3) ?
The derivative of x(2x-5^3) is (2x-5)^3+6x(2x-5)^2
What is the first derivative of x(2x-5^3) ?
The first derivative of x(2x-5^3) is (2x-5)^3+6x(2x-5)^2