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

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

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

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

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

Solution steps

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

Treat

x, z

as constants

Take the constant out:

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

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

Simplify

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

d er i v a t i v e f (x) = \frac{1}{x} + \frac{1}{x ^{2}} + \frac{1}{x ^{3}}

\frac{d}{d x} (2 lo g_{10} (x) - 3 x)

\int \frac{2 x ^{2}}{4 x - x ^{2}} d x

d er i v a t i v e \frac{3 x + 4}{3 x - 4}

x (y + 1) d x + y (x - 1) d y = 0

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