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Popular >

derivative of ln(x)cos(x)

Solution

derivative of

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

tangent of f(x)=(1+4x)^{(3/2)},\at x=2 tangent of

f (x) = (1 + 4 x)^{(\frac{3}{2})}, at x = 2

tangent of 6x^2-4x tangent of

6 x^{2} - 4 x

integral of 1/(x^9)

\int \frac{1}{x ^{9}} d x

inverse oflaplace 2/((s^2+40s+400))inverse laplace

\frac{2}{( s ^{2} + 40 s + 400 )}

area 2x+5,x^2+2x+1,[-2,2]area

2 x + 5, x^{2} + 2 x + 1, [- 2, 2]

Frequently Asked Questions (FAQ)

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