What is (\partial)/(\partial x)(sin(pi(3x-5y))) ?

The answer to (\partial)/(\partial x)(sin(pi(3x-5y))) is cos(pi(3x-5y))*3pi

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(\partial)/(\partial x)(sin(pi(3x-5y)))

\frac{\partial}{\partial x} (sin (π (3 x - 5 y)))

cos (π (3 x - 5 y)) \cdot 3 π

Solution steps

\frac{\partial}{\partial x} (sin (π (3 x - 5 y)))

Treat

y

as a constant

Apply the chain rule:

cos (π (3 x - 5 y)) \frac{\partial}{\partial x} (π (3 x - 5 y))

= cos (π (3 x - 5 y)) \frac{\partial}{\partial x} (π (3 x - 5 y))

\frac{\partial}{\partial x} (π (3 x - 5 y)) = 3 π

= cos (π (3 x - 5 y)) \cdot 3 π

\int \frac{t ^{3}}{t ^{4} + 9} d t

\frac{1}{1 + \frac{1}{5} x ^{3}}

\frac{\partial}{\partial y} (2 x e^{x^{2} + y^{2}})

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

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

What is (\partial)/(\partial x)(sin(pi(3x-5y))) ?
The answer to (\partial)/(\partial x)(sin(pi(3x-5y))) is cos(pi(3x-5y))*3pi