What is the derivative of (x^2-1(x^3+3x)) ?

The derivative of (x^2-1(x^3+3x)) is 5x^4+6x^2-3

What is the first derivative of (x^2-1(x^3+3x)) ?

The first derivative of (x^2-1(x^3+3x)) is 5x^4+6x^2-3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

5 x^{4} + 6 x^{2} - 3

Solution steps

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

Apply the Product Rule:

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

f = x^{2} - 1, g = x^{3} + 3 x

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

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

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

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

Simplify

2 x (x^{3} + 3 x) + (3 x^{2} + 3) (x^{2} - 1) : 5 x^{4} + 6 x^{2} - 3

= 5 x^{4} + 6 x^{2} - 3

(y^{2})^{^{'}}

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

\frac{d y}{d x} y = x^{- 12}

\frac{\partial}{\partial y} (x^{2} y + e^{x y})

\frac{d}{d x} (x + 6)

What is the derivative of (x^2-1(x^3+3x)) ?
The derivative of (x^2-1(x^3+3x)) is 5x^4+6x^2-3
What is the first derivative of (x^2-1(x^3+3x)) ?
The first derivative of (x^2-1(x^3+3x)) is 5x^4+6x^2-3