What is (\partial)/(\partial x)(xye^z+x-z^2-3) ?

The answer to (\partial)/(\partial x)(xye^z+x-z^2-3) is e^zy+1

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(\partial)/(\partial x)(xye^z+x-z^2-3)

\frac{\partial}{\partial x} (x y e^{z} + x - z^{2} - 3)

e^{z} y + 1

Solution steps

\frac{\partial}{\partial x} (x y e^{z} + x - z^{2} - 3)

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x y e^{z}) + \frac{\partial}{\partial x} (x) - \frac{\partial}{\partial x} (z^{2}) - \frac{\partial}{\partial x} (3)

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

\frac{\partial}{\partial x} (x) = 1

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

\frac{\partial}{\partial x} (3) = 0

= y e^{z} + 1 - 0 - 0

Simplify

= e^{z} y + 1

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

\int sin^{3} (10 x) d x

y = x^{2} - x + 4, at x = 4

x \to - 0 lim (\frac{1}{1 + e ^{\frac{1}{x}}})

What is (\partial)/(\partial x)(xye^z+x-z^2-3) ?
The answer to (\partial)/(\partial x)(xye^z+x-z^2-3) is e^zy+1