What is (\partial)/(\partial y)(xcos(x+2y)) ?

The answer to (\partial)/(\partial y)(xcos(x+2y)) is -2xsin(x+2y)

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(\partial)/(\partial y)(xcos(x+2y))

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

- 2 x sin (x + 2 y)

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= x (- sin (x + 2 y) \cdot 2)

Simplify

= - 2 x sin (x + 2 y)

f (x) = \frac{1}{x + 1}, at x = 4

\int \frac{1}{( x ^{2} - 4 )} d x

\frac{d}{d x} ((2 x)^{6 x})

\frac{d}{d x} ((x^{5} - 4 x^{3} - 7)^{8})

\frac{d}{d x} (\frac{0.07 e ^{x}}{sin ( x )})

What is (\partial)/(\partial y)(xcos(x+2y)) ?
The answer to (\partial)/(\partial y)(xcos(x+2y)) is -2xsin(x+2y)