en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of ln(xsin(x))

Solution

\frac{d}{d x} (ln (x) sin (x))

Solution

\frac{sin ( x )}{x} + cos (x) ln (x)

Solution steps

\frac{d}{d x} (ln (x) sin (x))

Apply the Product Rule:

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

f = ln (x), g = sin (x)

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

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

\frac{d}{d x} (sin (x)) = cos (x)

= \frac{1}{x} sin (x) + cos (x) ln (x)

\frac{1}{x} sin (x) = \frac{sin ( x )}{x}

= \frac{sin ( x )}{x} + cos (x) ln (x)

Graph

Popular Examples

(d^2y)/(dx^2)=3e^{-x},y(0)=1,y^'(0)=4

\frac{d ^{2} y}{d x ^{2}} = 3 e^{- x}, y (0) = 1, y^{^{'}} (0) = 4

integral of 1 1/(x^2)

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

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

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

y^'-2x=4x^3,y(0)=1

y^{^{'}} - 2 x = 4 x^{3}, y (0) = 1

derivative of 7xln((16x)/(16x+1))derivative of

7 x ln (\frac{16 x}{16 x + 1})

Frequently Asked Questions (FAQ)

What is the derivative of ln(xsin(x)) ?
The derivative of ln(xsin(x)) is (sin(x))/x+cos(x)ln(x)
What is the first derivative of ln(xsin(x)) ?
The first derivative of ln(xsin(x)) is (sin(x))/x+cos(x)ln(x)