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Popular >

derivative of f(x)=sin(x)ln(6x)

Solution

derivative of

f (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}

Graph

Popular Examples

integral of e^{x^1}

\int e^{x^{1}} d x

derivative of (2x+5/(3x-2))

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

integral of sin(x)-2

\int sin (x) - 2 d x

limit as x approaches 1 of sqrt(x+5)

x \to 1 lim (x + 5)

derivative of (3x-1^5(2x+3)^4)

\frac{d}{d x} ((3 x - 1)^{5} (2 x + 3)^{4})

Frequently Asked Questions (FAQ)

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