What is (\partial)/(\partial x)(cos(pix)-x^2y+e^{xz}+yz) ?

The answer to (\partial)/(\partial x)(cos(pix)-x^2y+e^{xz}+yz) is -2xy+e^{xz}z-pisin(pix)

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(\partial)/(\partial x)(cos(pix)-x^2y+e^{xz}+yz)

\frac{\partial}{\partial x} (cos (π x) - x^{2} y + e^{x z} + yz)

- 2 x y + e^{x z} z - π sin (π x)

Solution steps

\frac{\partial}{\partial x} (cos (π x) - x^{2} y + e^{x z} + yz)

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (cos (π x)) - \frac{\partial}{\partial x} (x^{2} y) + \frac{\partial}{\partial x} (e^{x z}) + \frac{\partial}{\partial x} (yz)

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

\frac{\partial}{\partial x} (x^{2} y) = 2 y x

\frac{\partial}{\partial x} (e^{x z}) = e^{x z} z

\frac{\partial}{\partial x} (yz) = 0

= - sin (π x) π - 2 y x + e^{x z} z + 0

Simplify

= - 2 x y + e^{x z} z - π sin (π x)

f (x) = - e^{x} x + 2 e^{x}

\frac{d}{d x} (3 x^{2} cos (x) - x^{3} sin (x))

\int \frac{22}{( x ^{2} - 1 ) ^{2}} d x

x \to 0 lim (x (csc (x)))

\int sin^{3} (x) cos^{20} (x) d x

What is (\partial)/(\partial x)(cos(pix)-x^2y+e^{xz}+yz) ?
The answer to (\partial)/(\partial x)(cos(pix)-x^2y+e^{xz}+yz) is -2xy+e^{xz}z-pisin(pix)