What is (\partial)/(\partial x)(sin(x)+pi*cos(y)) ?

The answer to (\partial)/(\partial x)(sin(x)+pi*cos(y)) is cos(x)

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(\partial)/(\partial x)(sin(x)+pi*cos(y))

\frac{\partial}{\partial x} (sin (x) + π \cdot cos (y))

cos (x)

Solution steps

\frac{\partial}{\partial x} (sin (x) + π cos (y))

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (sin (x)) + \frac{\partial}{\partial x} (π cos (y))

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

\frac{\partial}{\partial x} (π cos (y)) = 0

= cos (x) + 0

Simplify

= cos (x)

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\int \frac{sin ( 21 x )}{1 + cos ^{2} ( 21 x )} d x

\int_{0}^{1} x (1 - x) d x

What is (\partial)/(\partial x)(sin(x)+pi*cos(y)) ?
The answer to (\partial)/(\partial x)(sin(x)+pi*cos(y)) is cos(x)