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

The derivative of f(x)=(2x^3+5x)(x-3)(x+2) is 10x^4-8x^3-21x^2-10x-30

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

The first derivative of f(x)=(2x^3+5x)(x-3)(x+2) is 10x^4-8x^3-21x^2-10x-30

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

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

10 x^{4} - 8 x^{3} - 21 x^{2} - 10 x - 30

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} ((x - 3) (x + 2)) = 2 x - 1

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

Simplify

(6 x^{2} + 5) (x - 3) (x + 2) + (2 x - 1) (2 x^{3} + 5 x) : 10 x^{4} - 8 x^{3} - 21 x^{2} - 10 x - 30

= 10 x^{4} - 8 x^{3} - 21 x^{2} - 10 x - 30

x \to π lim (3 cot (x))

\int \frac{15 e ^{5 r}}{e ^{5 r} + 2} d r

\int x^{2} \cdot ln (3 x) d x

y = - 3 cos (x), at x = \frac{3 π}{4}

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

What is the derivative of f(x)=(2x^3+5x)(x-3)(x+2) ?
The derivative of f(x)=(2x^3+5x)(x-3)(x+2) is 10x^4-8x^3-21x^2-10x-30
What is the first derivative of f(x)=(2x^3+5x)(x-3)(x+2) ?
The first derivative of f(x)=(2x^3+5x)(x-3)(x+2) is 10x^4-8x^3-21x^2-10x-30