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

The answer to (\partial)/(\partial x)(y^2sin(xy)) is y^3cos(yx)

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

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

y^{3} cos (y x)

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

= y^{3} cos (y x)

\int (5^{3 x} + cosh (x)) d x

x \to 3 lim (2^{x})

\int tan^{5} (x) sec^{9} (x) d x

\int \frac{8 x ^{2} + 9 x + 8}{( x ^{2} + 1 ) ^{2}} d x

n = 0 \sum \infty (\frac{3}{7})^{n}

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