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

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

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

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

y^{3} cos (x + y)

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

= y^{3} \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) = 1

= y^{3} cos (x + y) \cdot 1

Simplify

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

\frac{d}{d x} (\frac{x}{x ^{- 1} + 9})

\int (\frac{3 x ^{2}}{64 - x ^{2}}) d x

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

\int x 36 - x^{2} d x

\int \frac{e ^{t}}{( 1 + e ^{(2 t)} ) ^{(\frac{3}{2})}} d t

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