What is (\partial)/(\partial y)(1+y^2sin(2x)) ?

The answer to (\partial)/(\partial y)(1+y^2sin(2x)) is 2ysin(2x)

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(\partial)/(\partial y)(1+y^2sin(2x))

\frac{\partial}{\partial y} (1 + y^{2} sin (2 x))

2 y sin (2 x)

Solution steps

\frac{\partial}{\partial y} (1 + y^{2} sin (2 x))

Treat

x

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial y} (1) + \frac{\partial}{\partial y} (y^{2} sin (2 x))

\frac{\partial}{\partial y} (1) = 0

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

= 0 + 2 y sin (2 x)

Simplify

= 2 y sin (2 x)

\int x (1 + x^{2}) d x

\frac{d}{d x} (x^{3} - 12 x^{2} + 45 x)

x \to 2 lim (\frac{- 2}{0})

11 x - 4 y x^{2} + 1 y^{^{'}} = 0, y (0) = 2

\frac{d}{d x} (e^{\frac{x}{2}} \frac{1}{2})

What is (\partial)/(\partial y)(1+y^2sin(2x)) ?
The answer to (\partial)/(\partial y)(1+y^2sin(2x)) is 2ysin(2x)