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Popular >

derivative of sin(x)ln(x)

Solution

derivative of

sin (x) 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}

Popular Examples

derivative of f(x)=2sin^5(sqrt(x))derivative of

f (x) = 2 sin^{5} (x)

derivative of xsin(x^2)derivative of

x sin (x^{2})

y^{''}-4y^'+3y=-e^{-s},y(0)=0,y^'(0)=0

y^{^{''}} - 4 y^{^{'}} + 3 y = - e^{- s}, y (0) = 0, y^{^{'}} (0) = 0

derivative of arcsec(2x+2)derivative of

arcsec (2 x + 2)

integral of 8sin^4(x)cos^2(x)

\int 8 sin^{4} (x) cos^{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