What is the derivative of xcos(x-picos(x)+2sin(x)) ?

The derivative of xcos(x-picos(x)+2sin(x)) is -xsin(x)+pisin(x)+3cos(x)

What is the first derivative of xcos(x-picos(x)+2sin(x)) ?

The first derivative of xcos(x-picos(x)+2sin(x)) is -xsin(x)+pisin(x)+3cos(x)

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\frac{d}{d x} (x cos (x) - π cos (x) + 2 sin (x))

- x sin (x) + π sin (x) + 3 cos (x)

Solution steps

\frac{d}{d x} (x cos (x) - π cos (x) + 2 sin (x))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x cos (x)) - \frac{d}{d x} (π cos (x)) + \frac{d}{d x} (2 sin (x))

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

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

\frac{d}{d x} (2 sin (x)) = 2 cos (x)

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

Simplify

= - x sin (x) + π sin (x) + 3 cos (x)

What is the derivative of xcos(x-picos(x)+2sin(x)) ?
The derivative of xcos(x-picos(x)+2sin(x)) is -xsin(x)+pisin(x)+3cos(x)
What is the first derivative of xcos(x-picos(x)+2sin(x)) ?
The first derivative of xcos(x-picos(x)+2sin(x)) is -xsin(x)+pisin(x)+3cos(x)