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

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

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

derivative of x/4 derivative of

\frac{x}{4}

limit as x approaches-7 of (x^2-9)/(7-x)

x \to - 7 lim (\frac{x ^{2} - 9}{7 - x})

integral of 1/(xsqrt(4x^2-1))

\int \frac{1}{x 4 x ^{2} - 1} d x

limit as x approaches 1+of arctan(ln(x-1))

x \to 1 + lim (arctan (ln (x - 1)))

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