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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

x \to 0 - lim (\frac{∣ 8 x ∣}{x})

\frac{d}{d x} (x \cdot e^{- b x^{2}})

7 e^{x}

\frac{12 ( s + 2 )}{s ( s ^{2} + 9 )}

\int_{0}^{36} \frac{1}{36 - x} d x

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