What is the derivative of-sin(xln(cos(x))+xcos(x)) ?

The derivative of-sin(xln(cos(x))+xcos(x)) is -cos(x)ln(cos(x))+tan(x)sin(x)+cos(x)-xsin(x)

What is the first derivative of-sin(xln(cos(x))+xcos(x)) ?

The first derivative of-sin(xln(cos(x))+xcos(x)) is -cos(x)ln(cos(x))+tan(x)sin(x)+cos(x)-xsin(x)

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Popular >

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

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Simplify

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

y = e^{- 15 x}

\frac{d}{d x} (tan (x) sec (x))

sin (x) + \frac{8}{7} cot (x)

- 1

y = x ∣ x ∣

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