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

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

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

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

cos (x + 2 y) - x sin (x + 2 y)

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = cos (x + 2 y)

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

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

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

= 1 \cdot cos (x + 2 y) + (- sin (x + 2 y)) x

Simplify

= cos (x + 2 y) - x sin (x + 2 y)

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

f (x) = 5 sec (x)

g (x) = - 8 x^{2} - x + 8

x \to 2 lim (\frac{3}{x - 2})

ln (t^{2})

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