What is the derivative of (3x^7-4)(2x-5x^2) ?

The derivative of (3x^7-4)(2x-5x^2) is -135x^8+48x^7+40x-8

What is the first derivative of (3x^7-4)(2x-5x^2) ?

The first derivative of (3x^7-4)(2x-5x^2) is -135x^8+48x^7+40x-8

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

(3 x^{7} - 4) (2 x - 5 x^{2})

- 135 x^{8} + 48 x^{7} + 40 x - 8

Solution steps

\frac{d}{d x} ((3 x^{7} - 4) (2 x - 5 x^{2}))

Apply the Product Rule:

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

f = 3 x^{7} - 4, g = 2 x - 5 x^{2}

= \frac{d}{d x} (3 x^{7} - 4) (2 x - 5 x^{2}) + \frac{d}{d x} (2 x - 5 x^{2}) (3 x^{7} - 4)

\frac{d}{d x} (3 x^{7} - 4) = 21 x^{6}

\frac{d}{d x} (2 x - 5 x^{2}) = 2 - 10 x

= 21 x^{6} (2 x - 5 x^{2}) + (2 - 10 x) (3 x^{7} - 4)

Simplify

21 x^{6} (2 x - 5 x^{2}) + (2 - 10 x) (3 x^{7} - 4) : - 135 x^{8} + 48 x^{7} + 40 x - 8

= - 135 x^{8} + 48 x^{7} + 40 x - 8

x \to - 2 lim (1 + x)

x^{5} + 8

\int 2 tan^{2} (x) d x

\int \frac{1}{3} - e^{t} d t

\frac{\partial}{\partial x} (- 9 y sin (3 x))

What is the derivative of (3x^7-4)(2x-5x^2) ?
The derivative of (3x^7-4)(2x-5x^2) is -135x^8+48x^7+40x-8
What is the first derivative of (3x^7-4)(2x-5x^2) ?
The first derivative of (3x^7-4)(2x-5x^2) is -135x^8+48x^7+40x-8