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

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

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

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

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

Solution steps

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

Treat

x, z

as constants

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= 2 x z^{3} e^{y^{2}} \cdot 2 y

Simplify

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

x, at x = 1

\int x (x - 3) d x

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

f (x) = - \frac{7}{( x + 4 ) ^{2}}

f (t) = (1) (t^{3})

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