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

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

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

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

cos (π (5 x - y)) \cdot 5 π

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= cos (π (5 x - y)) \cdot 5 π

y^{2} y^{^{'}} = e^{x}

x \to \infty lim (f (x))

\frac{d}{d x} (3 x^{2} sin (x) + 3 x cos (x))

\frac{d}{d t} (a cos (3 t) + b sin (3 t))

\frac{\partial}{\partial a} (\frac{a}{sin ( θ )})

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