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

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

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

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

cos (π (6 x - y)) \cdot 6 π

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= cos (π (6 x - y)) \cdot 6 π

arctan (\frac{1 + t}{1 - t})

\frac{d}{d x} (- 2 (arctan (3 x) - arctan (2 x)) + x)

\int \frac{3}{60 - t} d t

\frac{8}{x ^{2} + 4}

f (x) = \frac{20 x}{x ^{2} - 5}

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