en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of sin(xln(2x))

Solution

\frac{d}{d x} (sin (x) ln (2 x))

Solution

cos (x) ln (2 x) + \frac{sin ( x )}{x}

Solution steps

\frac{d}{d x} (sin (x) ln (2 x))

Apply the Product Rule:

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

f = sin (x), g = ln (2 x)

= \frac{d}{d x} (sin (x)) ln (2 x) + \frac{d}{d x} (ln (2 x)) sin (x)

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

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

= cos (x) ln (2 x) + \frac{1}{x} sin (x)

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

= cos (x) ln (2 x) + \frac{sin ( x )}{x}

Popular Examples

derivative of x*e^{-3x}

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

integral of (cos(θ))/(1+sin^2(θ))

\int \frac{cos ( θ )}{1 + sin ^{2} ( θ )} d θ

integral of (1+ye^{xy})

\int (1 + y e^{x y}) d x

integral of 1/(x(ln(x))^2)

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

derivative of (e^x/(x^2+1))

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

Frequently Asked Questions (FAQ)

What is the derivative of sin(xln(2x)) ?
The derivative of sin(xln(2x)) is cos(x)ln(2x)+(sin(x))/x
What is the first derivative of sin(xln(2x)) ?
The first derivative of sin(xln(2x)) is cos(x)ln(2x)+(sin(x))/x