What is (\partial)/(\partial x)(5e^{xy}) ?

The answer to (\partial)/(\partial x)(5e^{xy}) is 5e^{xy}y

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(\partial)/(\partial x)(5e^{xy})

\frac{\partial}{\partial x} (5 e^{x y})

5 e^{x y} y

Solution steps

\frac{\partial}{\partial x} (5 e^{x y})

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \frac{\partial}{\partial x} (e^{x y})

Apply the chain rule:

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

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

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

= 5 e^{x y} y

\frac{d}{d x} (\frac{3 x - 5}{x ^{2} + 7})

\frac{d}{d x} (- 12 e^{- 2 x})

x \to 3 lim (\frac{3 x - 9}{x - 3})

\frac{d}{d x} (\frac{tan ( x )}{x ^{3}})

(f (5 x))^{2} - 2

What is (\partial)/(\partial x)(5e^{xy}) ?
The answer to (\partial)/(\partial x)(5e^{xy}) is 5e^{xy}y