en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of ln(x^3+6x^2)

Solution

\frac{d}{d x} (ln (x^{3} + 6 x^{2}))

Solution

\frac{3 ( x + 4 )}{x ( x + 6 )}

Solution steps

\frac{d}{d x} (ln (x^{3} + 6 x^{2}))

Apply the chain rule:

\frac{1}{x ^{3} + 6 x ^{2}} \frac{d}{d x} (x^{3} + 6 x^{2})

= \frac{1}{x ^{3} + 6 x ^{2}} \frac{d}{d x} (x^{3} + 6 x^{2})

\frac{d}{d x} (x^{3} + 6 x^{2}) = 3 x^{2} + 12 x

= \frac{1}{x ^{3} + 6 x ^{2}} (3 x^{2} + 12 x)

Simplify

\frac{1}{x ^{3} + 6 x ^{2}} (3 x^{2} + 12 x) : \frac{3 ( x + 4 )}{x ( x + 6 )}

= \frac{3 ( x + 4 )}{x ( x + 6 )}

Popular Examples

derivative of f(x)=sqrt(x^2-8x^2)derivative of

f (x) = x^{2} - 8 x^{2}

(\partial)/(\partial x)((w^Te^{-w^Tx})/((1+e^{-w^Tx))^2})

\frac{\partial}{\partial x} (\frac{w ^{T} e ^{- w^{T} x}}{( 1 + e ^{- w^{T} x} ) ^{2}})

inverse oflaplace 1/((b^2*(\frac{1+x){b^2}))}inverse laplace

\frac{1}{( b ^{2} \cdot ( \frac{1 + x}{b ^{2}} ) )}

limit as x approaches 1-of 1-x

x \to 1 - lim (1 - x)

integral of 1/(x^3sqrt(x^2-64))

\int \frac{1}{x ^{3} x ^{2} - 64} d x

Frequently Asked Questions (FAQ)

What is the derivative of ln(x^3+6x^2) ?
The derivative of ln(x^3+6x^2) is (3(x+4))/(x(x+6))
What is the first derivative of ln(x^3+6x^2) ?
The first derivative of ln(x^3+6x^2) is (3(x+4))/(x(x+6))