What is the derivative of f(x)=(x^2+1)^3(x^2+2)^6 ?

The derivative of f(x)=(x^2+1)^3(x^2+2)^6 is 6x(x^2+1)^2(x^2+2)^6+12x(x^2+2)^5(x^2+1)^3

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

The first derivative of f(x)=(x^2+1)^3(x^2+2)^6 is 6x(x^2+1)^2(x^2+2)^6+12x(x^2+2)^5(x^2+1)^3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

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

6 x (x^{2} + 1)^{2} (x^{2} + 2)^{6} + 12 x (x^{2} + 2)^{5} (x^{2} + 1)^{3}

Solution steps

\frac{d}{d x} ((x^{2} + 1)^{3} (x^{2} + 2)^{6})

Apply the Product Rule:

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

f = (x^{2} + 1)^{3}, g = (x^{2} + 2)^{6}

= \frac{d}{d x} ((x^{2} + 1)^{3}) (x^{2} + 2)^{6} + \frac{d}{d x} ((x^{2} + 2)^{6}) (x^{2} + 1)^{3}

\frac{d}{d x} ((x^{2} + 1)^{3}) = 6 x (x^{2} + 1)^{2}

\frac{d}{d x} ((x^{2} + 2)^{6}) = 12 x (x^{2} + 2)^{5}

= 6 x (x^{2} + 1)^{2} (x^{2} + 2)^{6} + 12 x (x^{2} + 2)^{5} (x^{2} + 1)^{3}

\frac{d}{d x} (x lo g_{10} (\frac{2}{x}))

\int \frac{x ^{2} - 1}{x} d x

\int \frac{- x + 1}{x ^{2} + 1} d x

(\frac{1}{3})^{x}

\int_{0}^{1} 2 x + 1 d x

What is the derivative of f(x)=(x^2+1)^3(x^2+2)^6 ?
The derivative of f(x)=(x^2+1)^3(x^2+2)^6 is 6x(x^2+1)^2(x^2+2)^6+12x(x^2+2)^5(x^2+1)^3
What is the first derivative of f(x)=(x^2+1)^3(x^2+2)^6 ?
The first derivative of f(x)=(x^2+1)^3(x^2+2)^6 is 6x(x^2+1)^2(x^2+2)^6+12x(x^2+2)^5(x^2+1)^3