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

The answer to (\partial)/(\partial y)(2xsin(x^2y)) is 2x^3cos(x^2y)

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

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

2 x^{3} cos (x^{2} y)

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

= 2 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) = x^{2}

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

Simplify

2 x cos (x^{2} y) x^{2} : 2 x^{3} cos (x^{2} y)

= 2 x^{3} cos (x^{2} y)

\frac{d}{d x} (5 x^{2} + 3 x - 2)

(- 8, - 14), (61, - 32)

- \frac{d y}{d x} = 4 x^{3} y

h \to 0 lim (\frac{1}{2 ^{h}})

\frac{d}{d a} (\frac{a}{a ^{2} + b ^{2}})

What is (\partial)/(\partial y)(2xsin(x^2y)) ?
The answer to (\partial)/(\partial y)(2xsin(x^2y)) is 2x^3cos(x^2y)