What is (\partial)/(\partial x)(x^2sin(3x-2y)) ?

The answer to (\partial)/(\partial x)(x^2sin(3x-2y)) is 2xsin(3x-2y)+cos(3x-2y)*3x^2

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(\partial)/(\partial x)(x^2sin(3x-2y))

\frac{\partial}{\partial x} (x^{2} sin (3 x - 2 y))

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

Solution steps

\frac{\partial}{\partial x} (x^{2} sin (3 x - 2 y))

Treat

y

as a constant

Apply the Product Rule:

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

f = x^{2}, g = sin (3 x - 2 y)

= \frac{\partial}{\partial x} (x^{2}) sin (3 x - 2 y) + \frac{\partial}{\partial x} (sin (3 x - 2 y)) x^{2}

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

\frac{\partial}{\partial x} (sin (3 x - 2 y)) = cos (3 x - 2 y) \cdot 3

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

What is (\partial)/(\partial x)(x^2sin(3x-2y)) ?
The answer to (\partial)/(\partial x)(x^2sin(3x-2y)) is 2xsin(3x-2y)+cos(3x-2y)*3x^2