What is (\partial)/(\partial y)(3ycos(pix)+2xz) ?

The answer to (\partial)/(\partial y)(3ycos(pix)+2xz) is 3cos(pix)

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(\partial)/(\partial y)(3ycos(pix)+2xz)

\frac{\partial}{\partial y} (3 y cos (π x) + 2 x z)

3 cos (π x)

Solution steps

\frac{\partial}{\partial y} (3 y cos (π x) + 2 x z)

Treat

x, z

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (3 y cos (π x)) + \frac{\partial}{\partial y} (2 x z)

\frac{\partial}{\partial y} (3 y cos (π x)) = 3 cos (π x)

\frac{\partial}{\partial y} (2 x z) = 0

= 3 cos (π x) + 0

Simplify

= 3 cos (π x)

y^{^{'}} = \frac{3}{x} (y^{2} + y), y (4) = 2

\int \frac{1}{v} d v

5 \cdot e^{- 3 x} \cdot sin (5 x) \cdot x

x \to 3 lim (5 - x)

\frac{1}{16} tan^{2} (x) + cos (x)

What is (\partial)/(\partial y)(3ycos(pix)+2xz) ?
The answer to (\partial)/(\partial y)(3ycos(pix)+2xz) is 3cos(pix)