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

The answer to (\partial)/(\partial x)(e^{5xy}5y) is 25e^{5xy}y^2

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

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

25 e^{5 x y} y^{2}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= 5 y e^{5 x y} \cdot 5 y

Simplify

5 y e^{5 x y} \cdot 5 y : 25 e^{5 x y} y^{2}

= 25 e^{5 x y} y^{2}

\frac{1}{x ^{2} - 1}

\frac{d}{d x} (1 + \frac{1}{x})

\frac{10}{s ^{2}} - 1

f (x) = (2 x^{2} + 4 x)^{3}

x y^{^{'}} = y + 8 x^{2} sin (x), y (π) = 0

What is (\partial)/(\partial x)(e^{5xy}5y) ?
The answer to (\partial)/(\partial x)(e^{5xy}5y) is 25e^{5xy}y^2