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Popular >

derivative of xsin(ln(x))

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

Popular Examples

sum from n=0 to infinity of 1/(n+19)

n = 0 \sum \infty \frac{1}{n + 19}

tangent of x^2+9x tangent of

x^{2} + 9 x

integral of (x-x^3)^2

\int (x - x^{3})^{2} d x

derivative of y=(6x^2-12x+12)e^{-8x}derivative of

y = (6 x^{2} - 12 x + 12) e^{- 8 x}

(d^2)/(dx^2)(sqrt(x^2+1))

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

Frequently Asked Questions (FAQ)

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