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Popular >

derivative of ln(xcos(x))

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

Popular Examples

x^2y^{''}+3xy^'-15y=0

x^{2} y^{^{''}} + 3 x y^{^{'}} - 15 y = 0

inverse oflaplace 6/(s^2+5s+6)inverse laplace

\frac{6}{s ^{2} + 5 s + 6}

limit as x approaches 4 of (x^2+x)/(x+1)

x \to 4 lim (\frac{x ^{2} + x}{x + 1})

area y=17-x^2,x=0,y=0 area

y = 17 - x^{2}, x = 0, y = 0

integral of ((x^2-1))/((x^2+1))

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

Frequently Asked Questions (FAQ)

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