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

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

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

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

\frac{1}{x} + y^{3}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= \frac{1}{x} + y^{3}

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