What is (\partial)/(\partial y)(x*sin(x+y)) ?

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

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(\partial)/(\partial y)(x*sin(x+y))

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

(x^{2} + 6) y^{^{'}} = x y

- 4 y^{^{''}} + 16 y = 0

\frac{d}{d x} (ln (x \cdot y))

\int x^{4} e^{x^{5}} d x

5 x sin (x^{2})

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