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

The derivative of xsin(x+cos(x)) is xcos(x)

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

The first derivative of xsin(x+cos(x)) is xcos(x)

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

x cos (x)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

= x cos (x)

\int 1 - cos (t) d t

\int 13 + 12 x - x^{2} d x

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

y^{^{'}} = 2 y + x^{2} + 7

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

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