What is (\partial)/(\partial y)(3x^2e^{x^2y}) ?

The answer to (\partial)/(\partial y)(3x^2e^{x^2y}) is 3e^{x^2y}x^4

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(\partial)/(\partial y)(3x^2e^{x^2y})

\frac{\partial}{\partial y} (3 x^{2} e^{x^{2} y})

3 e^{x^{2} y} x^{4}

Solution steps

\frac{\partial}{\partial y} (3 x^{2} e^{x^{2} y})

Treat

x

as a constant

Take the constant out:

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

= 3 x^{2} \frac{\partial}{\partial y} (e^{x^{2} y})

Apply the chain rule:

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

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

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

= 3 x^{2} e^{x^{2} y} x^{2}

Simplify

3 x^{2} e^{x^{2} y} x^{2} : 3 e^{x^{2} y} x^{4}

= 3 e^{x^{2} y} x^{4}

f (x) = cos (x), 0, \frac{π}{2}

x \to \infty lim (- 3 x^{2} + 5)

\int x e^{x^{- 2}} d x

\frac{d}{d x} (\frac{3}{x ^{2} + 1})

\frac{d}{d x} (\frac{1}{x ^{6}} + \frac{1}{x ^{7}})

What is (\partial)/(\partial y)(3x^2e^{x^2y}) ?
The answer to (\partial)/(\partial y)(3x^2e^{x^2y}) is 3e^{x^2y}x^4