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

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

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

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

cos (π (3 x - 2 y)) \cdot 3 π

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

cos (π (3 x - 2 y)) \frac{\partial}{\partial x} (π (3 x - 2 y))

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

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

= cos (π (3 x - 2 y)) \cdot 3 π

\frac{d}{d x} (x^{3} - 3 x^{2} + 3 x - 1)

\int 6 cos (x) d x

\int_{0}^{1} \frac{5}{x ^{2} + x - 6} d x

\frac{( x + 5 ) ( x ^{2} - 5 x + 25 )}{x ^{3}}

\int (14 x + 5) 7 x^{2} + 5 x d x

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