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

The derivative of xcos(x+sin(x)) is -xsin(x)+2cos(x)

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

The first derivative of xcos(x+sin(x)) is -xsin(x)+2cos(x)

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

- x sin (x) + 2 cos (x)

Solution steps

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

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

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

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

Simplify

= - x sin (x) + 2 cos (x)

x \to c lim (5 + 3 (- 2))

\int (2 x + 3) cos (x^{2} + 3 x) d x

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

\frac{\partial}{\partial x} (- 2 y e^{- x})

\int - sin (x) - cos (x) d x

What is the derivative of xcos(x+sin(x)) ?
The derivative of xcos(x+sin(x)) is -xsin(x)+2cos(x)
What is the first derivative of xcos(x+sin(x)) ?
The first derivative of xcos(x+sin(x)) is -xsin(x)+2cos(x)