What is (\partial)/(\partial x)((4xy-5)^2) ?

The answer to (\partial)/(\partial x)((4xy-5)^2) is 8y(4xy-5)

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(\partial)/(\partial x)((4xy-5)^2)

\frac{\partial}{\partial x} ((4 x y - 5)^{2})

8 y (4 x y - 5)

Solution steps

\frac{\partial}{\partial x} ((4 x y - 5)^{2})

Treat

y

as a constant

Apply the chain rule:

2 (4 x y - 5) \frac{\partial}{\partial x} (4 x y - 5)

= 2 (4 x y - 5) \frac{\partial}{\partial x} (4 x y - 5)

\frac{\partial}{\partial x} (4 x y - 5) = 4 y

= 2 (4 x y - 5) \cdot 4 y

Simplify

= 8 y (4 x y - 5)

e^{(\frac{x}{4})}, x = 4, y = 1

\frac{d}{d t} (- 4 sin (t))

\int \frac{( x ^{3} )}{x ^{2} - 81} d x

x^{2}, - 1 \leq x \leq 2

\int \frac{- 5}{6 x} d x

What is (\partial)/(\partial x)((4xy-5)^2) ?
The answer to (\partial)/(\partial x)((4xy-5)^2) is 8y(4xy-5)