What is (\partial)/(\partial x)(xy^2+3xy+1/y) ?

The answer to (\partial)/(\partial x)(xy^2+3xy+1/y) is y^2+3y

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(\partial)/(\partial x)(xy^2+3xy+1/y)

\frac{\partial}{\partial x} (x y^{2} + 3 x y + \frac{1}{y})

y^{2} + 3 y

Solution steps

\frac{\partial}{\partial x} (x y^{2} + 3 x y + \frac{1}{y})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x y^{2}) + \frac{\partial}{\partial x} (3 x y) + \frac{\partial}{\partial x} (\frac{1}{y})

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

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

\frac{\partial}{\partial x} (\frac{1}{y}) = 0

= y^{2} + 3 y + 0

Simplify

= y^{2} + 3 y

\int \frac{1}{( sin ( x ) - cos ( x ) - 1 )} d x

f (x) = ln (3) x^{2}

\frac{x ^{9} - 6 x x}{x}

\frac{d}{d x} (5^{x, x})

x^{5}

What is (\partial)/(\partial x)(xy^2+3xy+1/y) ?
The answer to (\partial)/(\partial x)(xy^2+3xy+1/y) is y^2+3y