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

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

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

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

x cos (x + 2 y) \cdot 2

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= x cos (x + 2 y) \cdot 2

y^{^{''}} - 2 y^{^{'}} - 8 y = 7 - e^{4 x}

f (x) = x^{3} + 9 x^{2} + 34 x + 15, at x = 7

cos (x^{2})

\frac{d}{d x} (e^{- x^{2}} + x)

g (x) = 3 x, at x = 4

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