What is (\partial)/(\partial x)(x^3sin(xy)) ?

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

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(\partial)/(\partial x)(x^3sin(xy))

\frac{\partial}{\partial x} (x^{3} sin (x y))

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

Solution steps

\frac{\partial}{\partial x} (x^{3} sin (x y))

Treat

y

as a constant

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{3}, g = sin (x y)

= \frac{\partial}{\partial x} (x^{3}) sin (x y) + \frac{\partial}{\partial x} (sin (x y)) x^{3}

\frac{\partial}{\partial x} (x^{3}) = 3 x^{2}

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

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

\int (1 - e^{- 10 t} - 10 t e^{- 10 t}) d t

y = 3 x, y = 3, x = 0

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

\frac{d}{d x} (arccsc (e^{x}))

\frac{\partial}{\partial y} (y^{4} cos (2 x))

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