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Popular >

derivative of sin(x)ln(2x)

Solution

derivative of

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}

Graph

Popular Examples

(\partial)/(\partial x)(45ysin(9x))

\frac{\partial}{\partial x} (45 y sin (9 x))

integral from 1 to 3 of (y^4+1/(4y^4))

\int_{1}^{3} (y^{4} + \frac{1}{4 y ^{4}}) d y

y^{''}+6y^'+25y=0,y(0)=a,y^'(0)=b

y^{^{''}} + 6 y^{^{'}} + 25 y = 0, y (0) = a, y^{^{'}} (0) = b

integral from 3 to 7 of 1

\int_{3}^{7} 1 d x

integral from 0 to 6 of 1/18 x

\int_{0}^{6} \frac{1}{18} x d x

Frequently Asked Questions (FAQ)

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