What is (\partial)/(\partial x)(x^2sin(4y)) ?

The answer to (\partial)/(\partial x)(x^2sin(4y)) is 2xsin(4y)

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(\partial)/(\partial x)(x^2sin(4y))

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

2 x sin (4 y)

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

= sin (4 y) \cdot 2 x^{2 - 1}

Simplify

= 2 x sin (4 y)

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

\frac{\partial}{\partial x} (- sin (x y) y)

y^{^{'}} - x y^{2} = 2 x y

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

\int x^{2} sin (9 x) d x

What is (\partial)/(\partial x)(x^2sin(4y)) ?
The answer to (\partial)/(\partial x)(x^2sin(4y)) is 2xsin(4y)