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Popular >

derivative of y=sin(x)ln(2x)

Solution

derivative of

y = sin (x) ln (2 x)

Solution

cos (x) ln (2 x) + \frac{sin ( x )}{x}

Solution steps

\frac{d}{d x} (sin (x) ln (2 x))

Apply the Product Rule:

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

f = sin (x), g = ln (2 x)

= \frac{d}{d x} (sin (x)) ln (2 x) + \frac{d}{d x} (ln (2 x)) sin (x)

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

\frac{d}{d x} (ln (2 x)) = \frac{1}{x}

= cos (x) ln (2 x) + \frac{1}{x} sin (x)

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

= cos (x) ln (2 x) + \frac{sin ( x )}{x}

Popular Examples

derivative of (6arctan(2x)/(5e^{3x)})

\frac{d}{d x} (\frac{6 arctan ( 2 x )}{5 e ^{3 x}})

laplacetransform t^3e^{3t}laplace transform

t^{3} e^{3 t}

integral of ln(x/x)

\int ln (\frac{x}{x}) d x

derivative of f(x)=ax^4+(a-9)x^2-9 derivative of

f (x) = a x^{4} + (a - 9) x^{2} - 9

sum from n=1 to infinity of (3n)/(n^2+4)

n = 1 \sum \infty \frac{3 n}{n ^{2} + 4}

Frequently Asked Questions (FAQ)

What is the derivative of y=sin(x)ln(2x) ?
The derivative of y=sin(x)ln(2x) is cos(x)ln(2x)+(sin(x))/x
What is the first derivative of y=sin(x)ln(2x) ?
The first derivative of y=sin(x)ln(2x) is cos(x)ln(2x)+(sin(x))/x