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

The answer to (\partial)/(\partial y)(x^2e^{5xy}) is 5e^{5xy}x^3

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(\partial)/(\partial y)(x^2e^{5xy})

\frac{\partial}{\partial y} (x^{2} e^{5 x y})

5 e^{5 x y} x^{3}

Solution steps

\frac{\partial}{\partial y} (x^{2} e^{5 x y})

Treat

x

as a constant

Take the constant out:

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

= x^{2} \frac{\partial}{\partial y} (e^{5 x y})

Apply the chain rule:

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

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

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

= x^{2} e^{5 x y} \cdot 5 x

Simplify

x^{2} e^{5 x y} \cdot 5 x : 5 e^{5 x y} x^{3}

= 5 e^{5 x y} x^{3}

y = - x^{2} - 2 x + 3, y = x^{2} - 1

- 2 (4 e^{- x^{2}} x^{3} - 6 e^{- x^{2}} x)

ln^{2} (2 x)

x \to 1 lim (\frac{∣ x - 1 ∣}{1 - x})

\frac{x ^{2} + 4 x + 3}{x}

What is (\partial)/(\partial y)(x^2e^{5xy}) ?
The answer to (\partial)/(\partial y)(x^2e^{5xy}) is 5e^{5xy}x^3