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

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

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

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

sin (3 x + 2 y) + 3 cos (3 x + 2 y) (x - y)

Solution steps

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

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

\frac{\partial}{\partial x} (x - y) = 1

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

= 1 \cdot sin (3 x + 2 y) + cos (3 x + 2 y) \cdot 3 (x - y)

Simplify

= sin (3 x + 2 y) + 3 cos (3 x + 2 y) (x - y)

\frac{6}{( s ^{2} ( s ^{2} + 8 s + 1 ) )}

y = ln ∣ x ∣

f (x) = x - 8, at x = 12

\int x^{2} + 4 e^{x} + C d x

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

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