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

The answer to (\partial)/(\partial x)(e^{x^2y}+x^2y) is e^{x^2y}*2yx+2yx

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

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

e^{x^{2} y} \cdot 2 y x + 2 y x

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= e^{x^{2} y} \cdot 2 y x + 2 y x

\frac{d}{d x} (- \frac{y}{x ^{2}})

\frac{\partial}{\partial x} (x^{5} + x y^{7} + 6)

f (x) = 4 cos (x), (\frac{π}{3}, 2)

\frac{\partial}{\partial w} (t e^{\frac{w}{t}})

What is (\partial)/(\partial x)(e^{x^2y}+x^2y) ?
The answer to (\partial)/(\partial x)(e^{x^2y}+x^2y) is e^{x^2y}*2yx+2yx