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

t a y l or \frac{1}{1 + \frac{1}{5} x ^{3}}

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

d er i v a t i v e \frac{( ( 2 x + 5 ) ^{7} )}{14}

\frac{d}{d x} (0.8 \cdot x^{4})

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

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