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

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

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

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

cos (π (6 x - 6 y)) \cdot 6 π

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= cos (π (6 x - 6 y)) \cdot 6 π

\frac{d}{d t} (t + 3)

\frac{d}{d x} (\frac{sin ( 2 x )}{cos ( 3 x )})

x \to 0 lim (e^{(- 3 x)})

\frac{\partial}{\partial y} (7 - x^{2} - 2 y^{2})

\int \frac{x ^{5}}{( x ^{3} + 1 ) ( x ^{3} + 8 )} d x

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