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Popular >

derivative of sin(xln(3x))

Solution

\frac{d}{d x} (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

integral of (x-3)/(x^3+3x^2+2x)

\int \frac{x - 3}{x ^{3} + 3 x ^{2} + 2 x} d x

integral of e^{-(2r)/a}

\int e^{- \frac{2 r}{a}} d r

limit as x approaches-9 of (x+10)/(x+9)

x \to - 9 lim (\frac{x + 10}{x + 9})

integral of (2x+3)^{-3}

\int (2 x + 3)^{- 3} d x

derivative of (5x^2+e^x/(x^3))

\frac{d}{d x} (\frac{5 x ^{2} + e ^{x}}{x ^{3}})

Frequently Asked Questions (FAQ)

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