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

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

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

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

x sin (2 y)

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

= sin (y) cos (y) \cdot 2 x^{2 - 1}

Simplify

sin (y) cos (y) \cdot 2 x^{2 - 1} : x sin (2 y)

= x sin (2 y)

\frac{d}{d v} (u^{2} - v^{2})

\int_{0}^{2} \frac{1}{x + 2} d x

x \to 0 lim (\frac{( cos ( 11 x ) - cos ( 6 x ) )}{x})

f (x) = x^{3} sin (x)

\frac{d}{d x} (\frac{x ^{2} - 6 x + 1}{( x ^{2} - 1 ) ^{2}})

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