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Popular >

derivative of cos(xln(x))

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

Popular Examples

derivative of (sin(6x^3)/(5x))

\frac{d}{d x} (\frac{sin ( 6 ) x ^{3}}{5 x})

integral of x(ln(x+1))

\int x (ln (x + 1)) d x

\frac{d}{d y} (e^{x y})

integral from 0 to pi/2 of 3cos^5(x)

\int_{0}^{\frac{π}{2}} 3 cos^{5} (x) d x

derivative of x^{1/4}-4e^x

\frac{d}{d x} (x^{\frac{1}{4}} - 4 e^{x})

Frequently Asked Questions (FAQ)

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