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

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

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

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

cos (π (5 x - 3 y)) \cdot 5 π

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= cos (π (5 x - 3 y)) \cdot 5 π

\int 1 + (\frac{4}{3 x ^{\frac{1}{3}}})^{2} d x

y = \frac{f ( x )}{x ^{2} + 2}

\frac{\partial}{\partial L} (L^{\frac{1}{4}})

\int \frac{2 - 8 x}{81 - 4 x ^{2}} d x

\frac{d x}{d t} = c_{1} x - c_{2} x^{2}

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