What is (\partial)/(\partial x)(sin(pi(5x-4y))) ?

The answer to (\partial)/(\partial x)(sin(pi(5x-4y))) is cos(pi(5x-4y))*5pi

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(\partial)/(\partial x)(sin(pi(5x-4y)))

\frac{\partial}{\partial x} (sin (π (5 x - 4 y)))

cos (π (5 x - 4 y)) \cdot 5 π

Solution steps

\frac{\partial}{\partial x} (sin (π (5 x - 4 y)))

Treat

y

as a constant

Apply the chain rule:

cos (π (5 x - 4 y)) \frac{\partial}{\partial x} (π (5 x - 4 y))

= cos (π (5 x - 4 y)) \frac{\partial}{\partial x} (π (5 x - 4 y))

\frac{\partial}{\partial x} (π (5 x - 4 y)) = 5 π

= cos (π (5 x - 4 y)) \cdot 5 π

x \to 2 - lim (\frac{x - 5}{x - 2})

(17 y^{2} - x y) d x + x^{2} d y = 0

\int \frac{e ^{3 x}}{5 + e ^{3 x}} d x

\frac{d}{d x} (arccsc (- 6 x^{2}))

x \to 0 lim (\frac{x}{x ^{2} + 3 x})

What is (\partial)/(\partial x)(sin(pi(5x-4y))) ?
The answer to (\partial)/(\partial x)(sin(pi(5x-4y))) is cos(pi(5x-4y))*5pi