What is (\partial)/(\partial y)(12y-5xcos(y)) ?

The answer to (\partial)/(\partial y)(12y-5xcos(y)) is 12+5xsin(y)

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(\partial)/(\partial y)(12y-5xcos(y))

\frac{\partial}{\partial y} (12 y - 5 x cos (y))

12 + 5 x sin (y)

Solution steps

\frac{\partial}{\partial y} (12 y - 5 x cos (y))

Treat

x

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial y} (12 y) - \frac{\partial}{\partial y} (5 x cos (y))

\frac{\partial}{\partial y} (12 y) = 12

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

= 12 - (- 5 x sin (y))

Simplify

= 12 + 5 x sin (y)

3 x + 2

\int cos^{4} (x s i) n^{2} x d x

\int \frac{x}{( 4 x ^{2} + 3 ) ^{6}} d x

e^{- t} (t^{2} + 1)

\frac{3}{2 3 x + 7}, at x = 6

What is (\partial)/(\partial y)(12y-5xcos(y)) ?
The answer to (\partial)/(\partial y)(12y-5xcos(y)) is 12+5xsin(y)