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(6x))

Solution

\frac{d}{d x} (sin (x) ln (6 x))

Solution

cos (x) ln (6 x) + \frac{sin ( x )}{x}

Solution steps

\frac{d}{d x} (sin (x) ln (6 x))

Apply the Product Rule:

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

f = sin (x), g = ln (6 x)

= \frac{d}{d x} (sin (x)) ln (6 x) + \frac{d}{d x} (ln (6 x)) sin (x)

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

\frac{d}{d x} (ln (6 x)) = \frac{1}{x}

= cos (x) ln (6 x) + \frac{1}{x} sin (x)

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

= cos (x) ln (6 x) + \frac{sin ( x )}{x}

Popular Examples

limit as x approaches 0+of x^7ln(x)

x \to 0 + lim (x^{7} ln (x))

limit as x approaches 0+of xln(x^7)

x \to 0 + lim (x ln (x^{7}))

integral of xsqrt(x-7)

\int x x - 7 d x

(\partial)/(\partial x)(sin(-2x+4y+z))

\frac{\partial}{\partial x} (sin (- 2 x + 4 y + z))

derivative of e^xsin(sqrt(x))

\frac{d}{d x} (e^{x} sin (x))

Frequently Asked Questions (FAQ)

What is the derivative of sin(xln(6x)) ?
The derivative of sin(xln(6x)) is cos(x)ln(6x)+(sin(x))/x
What is the first derivative of sin(xln(6x)) ?
The first derivative of sin(xln(6x)) is cos(x)ln(6x)+(sin(x))/x