What is (\partial)/(\partial y)(e^{xy^2}+4zy^3) ?

The answer to (\partial)/(\partial y)(e^{xy^2}+4zy^3) is e^{xy^2}*2xy+12zy^2

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(\partial)/(\partial y)(e^{xy^2}+4zy^3)

\frac{\partial}{\partial y} (e^{x y^{2}} + 4 z y^{3})

e^{x y^{2}} \cdot 2 x y + 12 z y^{2}

Solution steps

\frac{\partial}{\partial y} (e^{x y^{2}} + 4 z y^{3})

Treat

x, z

as constants

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial y} (e^{x y^{2}}) + \frac{\partial}{\partial y} (4 z y^{3})

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

\frac{\partial}{\partial y} (4 z y^{3}) = 12 z y^{2}

= e^{x y^{2}} \cdot 2 x y + 12 z y^{2}

\frac{d}{d x} (\frac{( x + 2 ) \cdot ( x + 4 )}{x ^{2} - 4 x + 20})

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

f (x) = 3 x^{2} - 4 x + 1

\frac{d}{d x} (sin (x) sec (x))

\int_{- 2}^{2} 2 d x

What is (\partial)/(\partial y)(e^{xy^2}+4zy^3) ?
The answer to (\partial)/(\partial y)(e^{xy^2}+4zy^3) is e^{xy^2}*2xy+12zy^2