What is (\partial)/(\partial x)(sin(pi(6x-3y))) ?

The answer to (\partial)/(\partial x)(sin(pi(6x-3y))) is cos(pi(6x-3y))*6pi

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(\partial)/(\partial x)(sin(pi(6x-3y)))

\frac{\partial}{\partial x} (sin (π (6 x - 3 y)))

cos (π (6 x - 3 y)) \cdot 6 π

Solution steps

\frac{\partial}{\partial x} (sin (π (6 x - 3 y)))

Treat

y

as a constant

Apply the chain rule:

cos (π (6 x - 3 y)) \frac{\partial}{\partial x} (π (6 x - 3 y))

= cos (π (6 x - 3 y)) \frac{\partial}{\partial x} (π (6 x - 3 y))

\frac{\partial}{\partial x} (π (6 x - 3 y)) = 6 π

= cos (π (6 x - 3 y)) \cdot 6 π

\frac{\partial}{\partial x} (x y - 5 x^{2} y)

\frac{d ^{2}}{d x ^{2}} f (x) = 5 x^{3} + 12 x^{2} + 8 x + 22

\frac{\partial}{\partial x} (4 (y - 1) (x - 4)^{3})

\int y e^{0.2 y} d y

\int_{0}^{π} 3 tan (\frac{x}{3}) d x

What is (\partial)/(\partial x)(sin(pi(6x-3y))) ?
The answer to (\partial)/(\partial x)(sin(pi(6x-3y))) is cos(pi(6x-3y))*6pi