What is the derivative of x^2ln(x^3+2x-1) ?

The derivative of x^2ln(x^3+2x-1) is 2xln(x^3+2x-1)+(x^2(3x^2+2))/(x^3+2x-1)

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

The first derivative of x^2ln(x^3+2x-1) is 2xln(x^3+2x-1)+(x^2(3x^2+2))/(x^3+2x-1)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

Solution steps

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

Apply the Product Rule:

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

f = x^{2}, g = ln (x^{3} + 2 x - 1)

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

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

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

y = (7 - 3 x^{3})^{3}

\int 16 e^{x} d x

\frac{f ( x )}{x ^{2} + 8}

\frac{d x}{d t} = 0.3 \cdot 10 - \frac{x}{40}

csc^{2} (θ) - 4

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