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Popular >

derivative of x^2sin(ln(x))

Solution

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

Solution

2 x sin (ln (x)) + x cos (ln (x))

Solution steps

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

Apply the Product Rule:

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

f = x^{2}, g = sin (ln (x))

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

\frac{d}{d x} (x^{2}) = 2 x

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

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

\frac{cos ( ln ( x ) )}{x} x^{2} = x cos (ln (x))

= 2 x sin (ln (x)) + x cos (ln (x))

Popular Examples

limit as x approaches 0 of sqrt(5-2x^2)

x \to 0 lim (5 - 2 x^{2})

limit as x approaches 3 of 2x^{-1}

x \to 3 lim (2 x^{- 1})

(dy)/(dx)= 1/4 sqrt(y)cos^2(sqrt(y))

\frac{d y}{d x} = \frac{1}{4} y cos^{2} (y)

integral of csc(x)tan(x)

\int csc (x) tan (x) d x

derivative of cos(xln(x^2+1))

\frac{d}{d x} (cos (x) ln (x^{2} + 1))

Frequently Asked Questions (FAQ)

What is the derivative of x^2sin(ln(x)) ?
The derivative of x^2sin(ln(x)) is 2xsin(ln(x))+xcos(ln(x))
What is the first derivative of x^2sin(ln(x)) ?
The first derivative of x^2sin(ln(x)) is 2xsin(ln(x))+xcos(ln(x))