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

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

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

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

x cos (x + y)

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= x cos (x + y) \cdot 1

Simplify

= x cos (x + y)

ln (6) x^{3}

\int 3 x^{2} - 2 d x

x^{2} + y^{2} = 100, (6, 8)

y = x^{2}, (- 0.6, 0.36)

\int - ln ∣ cos (x) ∣ d x

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