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

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

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

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

3 x^{2} sin (y)

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= sin (y) \cdot 3 x^{3 - 1}

Simplify

= 3 x^{2} sin (y)

\int \frac{1}{x ^{2}} x d x

\frac{d}{d x} ((2 x + 3 y)^{10})

\int 2 cos^{3} (6 x) d x

\int \frac{1}{z ^{3} z ^{2} - 49} d z

\frac{d}{d x} ((x + 4)^{\frac{2}{3}})

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