What is (\partial)/(\partial y)(x^2*sin(2y)) ?

The answer to (\partial)/(\partial y)(x^2*sin(2y)) is x^2cos(2y)*2

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(\partial)/(\partial y)(x^2*sin(2y))

\frac{\partial}{\partial y} (x^{2} \cdot sin (2 y))

x^{2} cos (2 y) \cdot 2

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= x^{2} cos (2 y) \cdot 2

What is (\partial)/(\partial y)(x^2*sin(2y)) ?
The answer to (\partial)/(\partial y)(x^2*sin(2y)) is x^2cos(2y)*2