What is (\partial)/(\partial y)(ln(5+x^2y^2)) ?

The answer to (\partial)/(\partial y)(ln(5+x^2y^2)) is (2x^2y)/(5+x^2y^2)

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(\partial)/(\partial y)(ln(5+x^2y^2))

\frac{\partial}{\partial y} (ln (5 + x^{2} y^{2}))

\frac{2 x ^{2} y}{5 + x ^{2} y ^{2}}

Solution steps

\frac{\partial}{\partial y} (ln (5 + x^{2} y^{2}))

Treat

x

as a constant

Apply the chain rule:

\frac{1}{5 + x ^{2} y ^{2}} \frac{\partial}{\partial y} (5 + x^{2} y^{2})

= \frac{1}{5 + x ^{2} y ^{2}} \frac{\partial}{\partial y} (5 + x^{2} y^{2})

\frac{\partial}{\partial y} (5 + x^{2} y^{2}) = 2 x^{2} y

= \frac{1}{5 + x ^{2} y ^{2}} \cdot 2 x^{2} y

Simplify

\frac{1}{5 + x ^{2} y ^{2}} \cdot 2 x^{2} y : \frac{2 x ^{2} y}{5 + x ^{2} y ^{2}}

= \frac{2 x ^{2} y}{5 + x ^{2} y ^{2}}

f (x) = 4 x - x^{2}, at x = 2

s = t^{3} - t^{2}

\frac{d}{d x} (16 x - x^{2})

t^{2} y^{^{''}} + 7 t y^{^{'}} + 9 y = 0

\int \frac{x ^{5}}{( x ^{3} + 1 ) ^{2}} d x

What is (\partial)/(\partial y)(ln(5+x^2y^2)) ?
The answer to (\partial)/(\partial y)(ln(5+x^2y^2)) is (2x^2y)/(5+x^2y^2)