en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of x^4(x-2^3)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Popular Examples

y^{''}-4y^'+3y=7x^3e^{(2x)}cos(2x)

y^{^{''}} - 4 y^{^{'}} + 3 y = 7 x^{3} e^{(2 x)} cos (2 x)

limit as x approaches 0 of 1/(e^x+1)

x \to 0 lim (\frac{1}{e ^{x} + 1})

integral of (sin^3(x))/(cos^7(x))

\int \frac{sin ^{3} ( x )}{cos ^{7} ( x )} d x

derivative of 4/3 pix^3

\frac{d}{d x} (\frac{4}{3} π x^{3})

integral from 1 to 100 of (37)/(x^3)

\int_{1}^{100} \frac{37}{x ^{3}} d x

Frequently Asked Questions (FAQ)

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