What is the derivative of cos(xln(cos(x))+xsin(x)) ?

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

What is the first derivative of cos(xln(cos(x))+xsin(x)) ?

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

\frac{d}{d x} (\frac{ln ( 4 x )}{4 x})

y = 4 - x^{2}, y = x + 2

\frac{\partial}{\partial y} (\frac{1}{x y})

\int \frac{x}{1 + x ^{2}} d x

\int \frac{3}{x ^{2}} - \frac{2}{x ^{3}} d x

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