What is (\partial)/(\partial x)(2cos(xy)) ?

The answer to (\partial)/(\partial x)(2cos(xy)) is -2ysin(xy)

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(\partial)/(\partial x)(2cos(xy))

\frac{\partial}{\partial x} (2 cos (x y))

- 2 y sin (x y)

Solution steps

\frac{\partial}{\partial x} (2 cos (x y))

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{\partial}{\partial x} (cos (x y))

Apply the chain rule:

- sin (x y) \frac{\partial}{\partial x} (x y)

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

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

= 2 (- sin (x y) y)

Simplify

= - 2 y sin (x y)

y = 2 x^{3} - 5 x, (1, - 3)

f (x) = 2 x^{3}, (- 1, - 2)

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

\frac{\partial}{\partial x} (\frac{x ^{3} b ^{4}}{c ^{2} d ^{4}})

y = 4 x, x = 0, y = 4

What is (\partial)/(\partial x)(2cos(xy)) ?
The answer to (\partial)/(\partial x)(2cos(xy)) is -2ysin(xy)