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

The derivative of y=(x^3-3x)(2x^2+3x+5) is 10x^4+12x^3-3x^2-18x-15

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

The first derivative of y=(x^3-3x)(2x^2+3x+5) is 10x^4+12x^3-3x^2-18x-15

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

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

10 x^{4} + 12 x^{3} - 3 x^{2} - 18 x - 15

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

= (3 x^{2} - 3) (2 x^{2} + 3 x + 5) + (4 x + 3) (x^{3} - 3 x)

Simplify

(3 x^{2} - 3) (2 x^{2} + 3 x + 5) + (4 x + 3) (x^{3} - 3 x) : 10 x^{4} + 12 x^{3} - 3 x^{2} - 18 x - 15

= 10 x^{4} + 12 x^{3} - 3 x^{2} - 18 x - 15

x \to 0 + lim (x (ln (x^{2})))

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

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

4 x^{2} + x y + 4 y^{2} = 9, (1, 1)

\frac{d}{d x} (3 x cot (4 x - 2))

What is the derivative of y=(x^3-3x)(2x^2+3x+5) ?
The derivative of y=(x^3-3x)(2x^2+3x+5) is 10x^4+12x^3-3x^2-18x-15
What is the first derivative of y=(x^3-3x)(2x^2+3x+5) ?
The first derivative of y=(x^3-3x)(2x^2+3x+5) is 10x^4+12x^3-3x^2-18x-15