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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

\int \frac{6 x ^{3}}{x ^{2} + 9} d x

t \to - 1 lim (t^{2} - 1)

\int sin (5 x) \cdot cos (2 x) d x

f (t) = ln (t^{9} + 5)

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