What is (\partial)/(\partial x)(yx-ln(x^3y+6x)) ?

The answer to (\partial)/(\partial x)(yx-ln(x^3y+6x)) is y-(3yx^2+6)/(yx^3+6x)

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(\partial)/(\partial x)(yx-ln(x^3y+6x))

\frac{\partial}{\partial x} (y x - ln (x^{3} y + 6 x))

y - \frac{3 y x ^{2} + 6}{y x ^{3} + 6 x}

Solution steps

\frac{\partial}{\partial x} (y x - ln (x^{3} y + 6 x))

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (y x) - \frac{\partial}{\partial x} (ln (x^{3} y + 6 x))

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

\frac{\partial}{\partial x} (ln (x^{3} y + 6 x)) = \frac{3 y x ^{2} + 6}{y x ^{3} + 6 x}

= y - \frac{3 y x ^{2} + 6}{y x ^{3} + 6 x}

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

\int e^{s i n (x)} 7 cos (x) d x

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

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

x \to 0 + lim (x ln (x^{5}))

What is (\partial)/(\partial x)(yx-ln(x^3y+6x)) ?
The answer to (\partial)/(\partial x)(yx-ln(x^3y+6x)) is y-(3yx^2+6)/(yx^3+6x)