en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of sin(x)ln(3x)

Solution

derivative of

sin (x) ln (3 x)

Solution

cos (x) ln (3 x) + \frac{sin ( x )}{x}

Solution steps

\frac{d}{d x} (sin (x) ln (3 x))

Apply the Product Rule:

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

f = sin (x), g = ln (3 x)

= \frac{d}{d x} (sin (x)) ln (3 x) + \frac{d}{d x} (ln (3 x)) sin (x)

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

\frac{d}{d x} (ln (3 x)) = \frac{1}{x}

= cos (x) ln (3 x) + \frac{1}{x} sin (x)

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

= cos (x) ln (3 x) + \frac{sin ( x )}{x}

Popular Examples

tangent of f(x)=-2x^5+11x^3,\at x=-2 tangent of

f (x) = - 2 x^{5} + 11 x^{3}, at x = - 2

y^{''}+3y^'+y=0

y^{^{''}} + 3 y^{^{'}} + y = 0

integral from 2 to infinity of 1/(e^x)

\int_{2}^{\infty} \frac{1}{e ^{x}} d x

limit as t approaches-2 of (t+2)/(t^2-4)

t \to - 2 lim (\frac{t + 2}{t ^{2} - 4})

x(dy)/(dx)+10y=9y^2,y(1)=-1

x \frac{d y}{d x} + 10 y = 9 y^{2}, y (1) = - 1

Frequently Asked Questions (FAQ)

What is the derivative of sin(x)ln(3x) ?
The derivative of sin(x)ln(3x) is cos(x)ln(3x)+(sin(x))/x
What is the first derivative of sin(x)ln(3x) ?
The first derivative of sin(x)ln(3x) is cos(x)ln(3x)+(sin(x))/x