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

The answer to (\partial)/(\partial y)(3x^2y+e^y) is 3x^2+e^y

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(\partial)/(\partial y)(3x^2y+e^y)

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

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

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

y = 8 x + 6 x^{\frac{3}{4}}

\frac{d y}{d t} = \frac{t}{t ^{2} y + y}, y (0) = - 9

\frac{\partial}{\partial z} (x^{2} - x yz)

y^{^{''}} - y^{^{'}} - 42 y = 0

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

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