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

The answer to (\partial)/(\partial y)(3xz^3e^{y^2}) is 6e^{y^2}xz^3y

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

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

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

Solution steps

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

Treat

x, z

as constants

Take the constant out:

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

= 3 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

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

Simplify

= 6 e^{y^{2}} x z^{3} y

x \to 2 lim (4 x^{2} + x + 4)

\int_{0}^{\frac{π}{6}} (6 sec^{2} (x)) d x

2 y^{^{''}} + 4 y^{^{'}} - 7 y = 7 cos (2 x)

\int 1 + x d x

f (x) = e^{3 x}, at x = \frac{1}{3} ln (5)

What is (\partial)/(\partial y)(3xz^3e^{y^2}) ?
The answer to (\partial)/(\partial y)(3xz^3e^{y^2}) is 6e^{y^2}xz^3y