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

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

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(\partial)/(\partial x)(xy+2x-ln(x^2y))

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

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

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

\frac{d}{d x} (\frac{5}{( 2 x ) ^{3}} + 2 cos (x))

\int (4 x)^{2} d x

\int_{4}^{8} t^{2} ln (3 t) d t

\int \frac{1}{6 x ( 3 + x )} d x

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