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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

\frac{1}{3 x + x ^{2} y ^{2}} \frac{\partial}{\partial x} (3 x + x^{2} y^{2})

= \frac{1}{3 x + x ^{2} y ^{2}} \frac{\partial}{\partial x} (3 x + x^{2} y^{2})

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

= \frac{1}{3 x + x ^{2} y ^{2}} (3 + 2 y^{2} x)

Simplify

\frac{1}{3 x + x ^{2} y ^{2}} (3 + 2 y^{2} x) : \frac{3 + 2 x y ^{2}}{3 x + x ^{2} y ^{2}}

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

\frac{\partial}{\partial x} (1 - \frac{4}{y} + x)

θ

\frac{\partial}{\partial y} (2 z^{2} sin (y))

e^{s}

2 cos (7 x), sin (14 x)

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