What is (\partial)/(\partial x)((xy-1)^2) ?

The answer to (\partial)/(\partial x)((xy-1)^2) is 2(xy-1)y

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(\partial)/(\partial x)((xy-1)^2)

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

2 (x y - 1) y

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

2 (x y - 1) \frac{\partial}{\partial x} (x y - 1)

= 2 (x y - 1) \frac{\partial}{\partial x} (x y - 1)

\frac{\partial}{\partial x} (x y - 1) = y

= 2 (x y - 1) y

\int \frac{x ^{4} + 4}{x ^{3}} d x

y^{^{''}} + 3 y^{^{'}} + 2 y = e^{- 2 t}

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

(sin (x) sin (2 x) sin (3 x))^{^{'}}

y = e^{x} sin (2 x)

What is (\partial)/(\partial x)((xy-1)^2) ?
The answer to (\partial)/(\partial x)((xy-1)^2) is 2(xy-1)y