What is (\partial)/(\partial x)(ln(2x)+5y^3) ?

The answer to (\partial)/(\partial x)(ln(2x)+5y^3) is 1/x

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(\partial)/(\partial x)(ln(2x)+5y^3)

\frac{\partial}{\partial x} (ln (2 x) + 5 y^{3})

\frac{1}{x}

Solution steps

\frac{\partial}{\partial x} (ln (2 x) + 5 y^{3})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (ln (2 x)) + \frac{\partial}{\partial x} (5 y^{3})

\frac{\partial}{\partial x} (ln (2 x)) = \frac{1}{x}

\frac{\partial}{\partial x} (5 y^{3}) = 0

= \frac{1}{x} + 0

Simplify

= \frac{1}{x}

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

\int_{0}^{1} \frac{1}{x ^{\frac{1}{2}}} d x

y^{^{'}} = - 10 y

\int_{0}^{\infty} e^{a x} d x

\frac{\partial}{\partial y} (x ln (5 x + 8 y))

What is (\partial)/(\partial x)(ln(2x)+5y^3) ?
The answer to (\partial)/(\partial x)(ln(2x)+5y^3) is 1/x