What is (\partial)/(\partial x)(2+yln(4+xy^2)) ?

The answer to (\partial)/(\partial x)(2+yln(4+xy^2)) is (y^3)/(y^2x+4)

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(\partial)/(\partial x)(2+yln(4+xy^2))

\frac{\partial}{\partial x} (2 + y ln (4 + x y^{2}))

\frac{y ^{3}}{y ^{2} x + 4}

Solution steps

\frac{\partial}{\partial x} (2 + y ln (4 + x y^{2}))

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (2) + \frac{\partial}{\partial x} (y ln (4 + x y^{2}))

\frac{\partial}{\partial x} (2) = 0

\frac{\partial}{\partial x} (y ln (4 + x y^{2})) = \frac{y ^{3}}{4 + y ^{2} x}

= 0 + \frac{y ^{3}}{4 + y ^{2} x}

Simplify

= \frac{y ^{3}}{y ^{2} x + 4}

What is (\partial)/(\partial x)(2+yln(4+xy^2)) ?
The answer to (\partial)/(\partial x)(2+yln(4+xy^2)) is (y^3)/(y^2x+4)