What is the derivative of sin(xln(4x)) ?

The derivative of sin(xln(4x)) is cos(x)ln(4x)+(sin(x))/x

What is the first derivative of sin(xln(4x)) ?

The first derivative of sin(xln(4x)) is cos(x)ln(4x)+(sin(x))/x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (sin (x) ln (4 x))

cos (x) ln (4 x) + \frac{sin ( x )}{x}

Solution steps

\frac{d}{d x} (sin (x) ln (4 x))

Apply the Product Rule:

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

f = sin (x), g = ln (4 x)

= \frac{d}{d x} (sin (x)) ln (4 x) + \frac{d}{d x} (ln (4 x)) sin (x)

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

\frac{d}{d x} (ln (4 x)) = \frac{1}{x}

= cos (x) ln (4 x) + \frac{1}{x} sin (x)

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

= cos (x) ln (4 x) + \frac{sin ( x )}{x}

What is the derivative of sin(xln(4x)) ?
The derivative of sin(xln(4x)) is cos(x)ln(4x)+(sin(x))/x
What is the first derivative of sin(xln(4x)) ?
The first derivative of sin(xln(4x)) is cos(x)ln(4x)+(sin(x))/x