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

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

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

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

\frac{d}{d x} (c e^{- 3 x})

f (x) = \frac{120 x ^{2}}{x ^{2} + 4}

\frac{d}{d x} (ln ∣ x + 2 ∣)

y^{^{'}} = \frac{y ^{2} + 1}{x ^{2} + 1}, y (0) = 1

\frac{d y}{d t} = a y

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