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Popular >

derivative of sin(x*ln(x))

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

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

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

Graph

Popular Examples

limit as x approaches 1 of (x^2-1)/(1-x)

x \to 1 lim (\frac{x ^{2} - 1}{1 - x})

taylor 1/(x-1),20 taylor

\frac{1}{x - 1}, 20

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f (x) = e^{7}

integral of tan(x)*sec^3(x)

\int tan (x) \cdot sec^{3} (x) d x

integral of e^{cos(x)}sin(2x)

\int e^{c o s (x)} sin (2 x) d x

Frequently Asked Questions (FAQ)

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