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

The derivative of (2x^2+1)^3(x^2-4)^2 is 12x(2x^2+1)^2(x^2-4)^2+4x(x^2-4)(2x^2+1)^3

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

The first derivative of (2x^2+1)^3(x^2-4)^2 is 12x(2x^2+1)^2(x^2-4)^2+4x(x^2-4)(2x^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

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

12 x (2 x^{2} + 1)^{2} (x^{2} - 4)^{2} + 4 x (x^{2} - 4) (2 x^{2} + 1)^{3}

Solution steps

\frac{d}{d x} ((2 x^{2} + 1)^{3} (x^{2} - 4)^{2})

Apply the Product Rule:

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

f = (2 x^{2} + 1)^{3}, g = (x^{2} - 4)^{2}

= \frac{d}{d x} ((2 x^{2} + 1)^{3}) (x^{2} - 4)^{2} + \frac{d}{d x} ((x^{2} - 4)^{2}) (2 x^{2} + 1)^{3}

\frac{d}{d x} ((2 x^{2} + 1)^{3}) = 12 x (2 x^{2} + 1)^{2}

\frac{d}{d x} ((x^{2} - 4)^{2}) = 4 x (x^{2} - 4)

= 12 x (2 x^{2} + 1)^{2} (x^{2} - 4)^{2} + 4 x (x^{2} - 4) (2 x^{2} + 1)^{3}

\int x (x - 1)^{6} d x

x \to 1 + lim (\frac{∣ x - 1 ∣}{1 - x})

\int \frac{θ}{y ^{2}} e^{- \frac{θ}{y}} d y

\int \frac{5 x ^{2} - 5 x}{2 x ^{3} - 3 x ^{2} + 12} d x

What is the derivative of (2x^2+1)^3(x^2-4)^2 ?
The derivative of (2x^2+1)^3(x^2-4)^2 is 12x(2x^2+1)^2(x^2-4)^2+4x(x^2-4)(2x^2+1)^3
What is the first derivative of (2x^2+1)^3(x^2-4)^2 ?
The first derivative of (2x^2+1)^3(x^2-4)^2 is 12x(2x^2+1)^2(x^2-4)^2+4x(x^2-4)(2x^2+1)^3