What is (\partial)/(\partial x)(e^{xy}+x^2z) ?

The answer to (\partial)/(\partial x)(e^{xy}+x^2z) is e^{xy}y+2zx

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(\partial)/(\partial x)(e^{xy}+x^2z)

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

e^{x y} y + 2 z x

Solution steps

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

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

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

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

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

= e^{x y} y + 2 z x

\int cos^{2} (θ) d θ

\frac{d ^{2}}{d x ^{2}} f (x) = \frac{7}{x + 4}, at x = 0

n = 1 \sum \infty \frac{n ^{2}}{n !}

3 x^{2} e^{y} + (x^{3} e^{y} - 1) \frac{d y}{d x} = 0

f (x) = x sin (π x), at x = 1

What is (\partial)/(\partial x)(e^{xy}+x^2z) ?
The answer to (\partial)/(\partial x)(e^{xy}+x^2z) is e^{xy}y+2zx