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

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

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(\partial)/(\partial x)(e^{2xy^2}+3x)

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (3 x) = 3

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

\frac{d}{d x} (\frac{3 ^{x}}{tan ( x )})

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

y = \frac{x ^{7}}{f ( x )}

\frac{d}{d x} (x^{7} e^{9 x})

f (x) = \frac{16 x}{x ^{2} + 16}

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