en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of x^3ln(x+1)

Solution

derivative of

x^{3} ln (x + 1)

Solution

3 x^{2} ln (x + 1) + \frac{x ^{3}}{x + 1}

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} (ln (x + 1)) = \frac{1}{x + 1}

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

\frac{1}{x + 1} x^{3} = \frac{x ^{3}}{x + 1}

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

Popular Examples

derivative of 2xcsc(x)-x^2cot(x)csc(x)derivative of

2 x csc (x) - x^{2} cot (x) csc (x)

area-3/8 x(x-8),10-x/2 ,2,8 area

- \frac{3}{8} x (x - 8), 10 - \frac{x}{2}, 2, 8

derivative of (2x^2+8x+6/(sqrt(x)))

\frac{d}{d x} (\frac{2 x ^{2} + 8 x + 6}{x})

integral from 3 to infinity of e^{-x/4}

\int_{3}^{\infty} e^{- \frac{x}{4}} d x

(\partial)/(\partial x)(9cos(ye^{xy})sin(x))

\frac{\partial}{\partial x} (9 cos (y e^{x y}) sin (x))

Frequently Asked Questions (FAQ)

What is the derivative of x^3ln(x+1) ?
The derivative of x^3ln(x+1) is 3x^2ln(x+1)+(x^3)/(x+1)
What is the first derivative of x^3ln(x+1) ?
The first derivative of x^3ln(x+1) is 3x^2ln(x+1)+(x^3)/(x+1)