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

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

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

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

2 y^{3}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 0 + 2 y^{3}

Simplify

= 2 y^{3}

y^{^{''}} + 9 y = 3 x e^{2 x}

t \to 0 lim (\frac{e ^{5 t} - 1}{t})

\int f^{- 1} (x) d x

4 cos (\frac{2 π}{3})

cos (a^{3} + x^{3})

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