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

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

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

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

3 x y^{2}

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial y} (ln (x)) = 0

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

= 0 + 3 x y^{2}

Simplify

= 3 x y^{2}

\int \frac{2 - x}{x ^{2} + x} d x

\int_{4}^{16} \frac{1}{8 - x} d x

x \to 2 + lim (\frac{8}{x - 2})

f (x) = 8 x^{2} - x^{3}, (2, 24)

(3, 4), (5, 8)

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