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(8x))

Solution

\frac{d}{d x} (sin (x) ln (8 x))

Solution

cos (x) ln (8 x) + \frac{sin ( x )}{x}

Solution steps

\frac{d}{d x} (sin (x) ln (8 x))

Apply the Product Rule:

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

f = sin (x), g = ln (8 x)

= \frac{d}{d x} (sin (x)) ln (8 x) + \frac{d}{d x} (ln (8 x)) sin (x)

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

\frac{d}{d x} (ln (8 x)) = \frac{1}{x}

= cos (x) ln (8 x) + \frac{1}{x} sin (x)

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

= cos (x) ln (8 x) + \frac{sin ( x )}{x}

Popular Examples

d/(d{x)}({x}^2+{y}{z})

\frac{d}{d x} (x^{2} + y z)

tangent of y=8x^2-x^3(2.24)tangent of

y = 8 x^{2} - x^{3} (2.24)

sum from n=0 to infinity of ((8^n))/(n!)

n = 0 \sum \infty \frac{( 8 ^{n} )}{n !}

y^{^{'}} + y = y^{2}

derivative of 30x^4y^7-24x^{12}y^3

\frac{d}{d x} (30 x^{4} y^{7} - 24 x^{12} y^{3})

Frequently Asked Questions (FAQ)

What is the derivative of sin(xln(8x)) ?
The derivative of sin(xln(8x)) is cos(x)ln(8x)+(sin(x))/x
What is the first derivative of sin(xln(8x)) ?
The first derivative of sin(xln(8x)) is cos(x)ln(8x)+(sin(x))/x