What is (\partial)/(\partial x)(yln(x)+xy^2) ?

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

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(\partial)/(\partial x)(yln(x)+xy^2)

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

\frac{y}{x} + y^{2}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= \frac{y}{x} + y^{2}

\int (\frac{1}{x ^{5}} - x^{5} - \frac{1}{3}) d x

\frac{2}{1 - x ^{2}}

y^{^{''}} - 4 y^{^{'}} + 4 y = 0, y (0) = 2, y^{^{'}} (0) = 7

n = 0 \sum \infty 1 (- \frac{1}{3})^{n}

\int 56 x d x

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