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Popular >

derivative of sin(x)ln(cos(x))

Solution

derivative of

sin (x) ln (cos (x))

Solution

cos (x) ln (cos (x)) - tan (x) sin (x)

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} (ln (cos (x))) = - tan (x)

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

Simplify

= cos (x) ln (cos (x)) - tan (x) sin (x)

Popular Examples

limit as x approaches-1 of 3x^2+4/(x^2)

x \to - 1 lim (3 x^{2} + \frac{4}{x ^{2}})

integral of-9cot(x)ln(sin(x))

\int - 9 cot (x) ln (sin (x)) d x

derivative of 4e^{3x^2}sin(cos(2x))

\frac{d}{d x} (4 e^{3 x^{2}} sin (cos (2 x)))

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\frac{d}{d x} (sin^{2} (x) - cos (x))

derivative of (x^2(e^x+5)/(e^xsqrt(x)))

\frac{d}{d x} (\frac{x ^{2} ( e ^{x} + 5 )}{e ^{x} x})

Frequently Asked Questions (FAQ)

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