What is the derivative of f(x)=ln(xe^{-3x}) ?

The derivative of f(x)=ln(xe^{-3x}) is 1/x-3

What is the first derivative of f(x)=ln(xe^{-3x}) ?

The first derivative of f(x)=ln(xe^{-3x}) is 1/x-3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

f (x) = ln (x e^{- 3 x})

\frac{1}{x} - 3

Solution steps

\frac{d}{d x} (ln (x e^{- 3 x}))

Simplify

ln (x e^{- 3 x}) : ln (x) - 3 x

= \frac{d}{d x} (ln (x) - 3 x)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (ln (x)) - \frac{d}{d x} (3 x)

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

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

= \frac{1}{x} - 3

\int \frac{1}{x ln ( 2 x )} d x

\frac{d ^{2}}{d y d x} (sin (x^{2} y^{2}))

\int x^{2} (x^{3} + 9)^{10} d x

\int \frac{2 x ^{2} - 8}{x ( x + 2 ) ^{3}} d x

12 x^{3} - 3 y^{2} x^{4} + 1 y^{^{'}} = 0

What is the derivative of f(x)=ln(xe^{-3x}) ?
The derivative of f(x)=ln(xe^{-3x}) is 1/x-3
What is the first derivative of f(x)=ln(xe^{-3x}) ?
The first derivative of f(x)=ln(xe^{-3x}) is 1/x-3