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

The answer to (\partial)/(\partial y)(ln(y)+2xy^3) is 1/y+6xy^2

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

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

\frac{1}{y} + 6 x y^{2}

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= \frac{1}{y} + 6 x y^{2}

n = 0 \sum \infty n! x^{n}

\int 2 sin (t) cos (t) e^{- c o s (t)} d t

y = x^{4} + 3 e^{x}

tan (x + 1)

\frac{d}{d x} (ln (3 + x))

What is (\partial)/(\partial y)(ln(y)+2xy^3) ?
The answer to (\partial)/(\partial y)(ln(y)+2xy^3) is 1/y+6xy^2