What is (\partial)/(\partial x)(sin(5pix+2y)) ?

The answer to (\partial)/(\partial x)(sin(5pix+2y)) is cos(5pix+2y)*5pi

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(\partial)/(\partial x)(sin(5pix+2y))

\frac{\partial}{\partial x} (sin (5 π x + 2 y))

cos (5 π x + 2 y) \cdot 5 π

Solution steps

\frac{\partial}{\partial x} (sin (5 π x + 2 y))

Treat

y

as a constant

Apply the chain rule:

cos (5 π x + 2 y) \frac{\partial}{\partial x} (5 π x + 2 y)

= cos (5 π x + 2 y) \frac{\partial}{\partial x} (5 π x + 2 y)

\frac{\partial}{\partial x} (5 π x + 2 y) = 5 π

= cos (5 π x + 2 y) \cdot 5 π

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

f (x) = x^{4} - 20 x^{2} + 64, at x = 2

x \to \frac{5 π}{2} lim (sec (x))

\frac{1}{2 r} + \frac{1}{6 r ^{\frac{5}{6}}}

\frac{( x + 2 ) ( 2 x + 4 )}{- x ^{2} - x - 2}

What is (\partial)/(\partial x)(sin(5pix+2y)) ?
The answer to (\partial)/(\partial x)(sin(5pix+2y)) is cos(5pix+2y)*5pi