en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of x^3(3x+1^6)

Solution

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

Solution

3 x^{2} (3 x + 1)^{6} + 18 (3 x + 1)^{5} x^{3}

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} ((3 x + 1)^{6}) = 18 (3 x + 1)^{5}

= 3 x^{2} (3 x + 1)^{6} + 18 (3 x + 1)^{5} x^{3}

Graph

Popular Examples

limit as x approaches-1 of (x^3-8)/(x-2)

x \to - 1 lim (\frac{x ^{3} - 8}{x - 2})

derivative of 5x^{4/3}

\frac{d}{d x} (5 x^{\frac{4}{3}})

derivative of (5x^2/(3x-1))

\frac{d}{d x} (\frac{5 x ^{2}}{3 x - 1})

integral of 1/(xsqrt(16+x^2))

\int \frac{1}{x 16 + x ^{2}} d x

(dy)/(dx)=(x+y-1)^2

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

Frequently Asked Questions (FAQ)

What is the derivative of x^3(3x+1^6) ?
The derivative of x^3(3x+1^6) is 3x^2(3x+1)^6+18(3x+1)^5x^3
What is the first derivative of x^3(3x+1^6) ?
The first derivative of x^3(3x+1^6) is 3x^2(3x+1)^6+18(3x+1)^5x^3