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

The answer to (\partial)/(\partial y)(5y^2e^{5xy}) is 5(2ye^{5xy}+e^{5xy}*5xy^2)

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

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

5 (2 y e^{5 x y} + e^{5 x y} \cdot 5 x y^{2})

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y^{2}, g = e^{5 x y}

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

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

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

= 5 (2 y e^{5 x y} + e^{5 x y} \cdot 5 x y^{2})

\int sin (wt) d t

x y^{^{'}} = \frac{1}{y ^{3}}

\int_{- 1}^{2} (- x^{2} + x + 2)^{2} d x

x \to \infty lim (\frac{x}{0})

(t^{2} + x^{2}) d t + t x d x = 0

What is (\partial)/(\partial y)(5y^2e^{5xy}) ?
The answer to (\partial)/(\partial y)(5y^2e^{5xy}) is 5(2ye^{5xy}+e^{5xy}*5xy^2)