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

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

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

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

e^{x y^{2}} y^{2} - \frac{2}{x}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (2 ln (x)) = \frac{2}{x}

\frac{\partial}{\partial x} (3 y) = 0

= e^{x y^{2}} y^{2} - \frac{2}{x} + 0

Simplify

= e^{x y^{2}} y^{2} - \frac{2}{x}

f (x) = 2 x sin (3 x)

x \to 2 lim (3 x - 4)

\frac{d}{d x} (3 x ln (x))

\frac{d}{d x} ((1 - x)^{2})

f (x) = \frac{4 x + x ^{2}}{( 2 + x ) ^{2}}

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