en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of x(4x-12)^3

Solution

derivative of

x (4 x - 12)^{3}

Solution

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

Solution steps

\frac{d}{d x} (x (4 x - 12)^{3})

Apply the Product Rule:

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

f = x, g = (4 x - 12)^{3}

= \frac{d x}{d x} (4 x - 12)^{3} + \frac{d}{d x} ((4 x - 12)^{3}) x

\frac{d x}{d x} = 1

\frac{d}{d x} ((4 x - 12)^{3}) = 12 (4 x - 12)^{2}

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

Simplify

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

Popular Examples

integral of 5sin(5x)sin(x)

\int 5 sin (5 x) sin (x) d x

integral of (x^3)/((9-x^4)^2)

\int \frac{x ^{3}}{( 9 - x ^{4} ) ^{2}} d x

derivative of f(x)=2x^e derivative of

f (x) = 2 x^{e}

integral of 4x+3x^2+12x^3+C

\int 4 x + 3 x^{2} + 12 x^{3} + C d x

integral of (cos(pi*x))/(sin(pi*x))

\int \frac{cos ( π \cdot x )}{sin ( π \cdot x )} d x

Frequently Asked Questions (FAQ)

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