Question

D/dx(sin x/2+cos x) = (a + b cos x)/(2+cos x)^2 find a and b.​

Answer 1

a = 1 and b = 2

Explanation:

Using the Quotient Rule>

d/dx[(sin x)/(2+cos x) ]

= [(2 + cos x) * cosx - sin x * - sin x)] / (2 + cos x)^2

= 2cos x + cos^2x + sin ^2 x) / (2 + cos x)^2

But cos^2x + sin^2x = 1 so we have:

(1 + 2 cos x) / (2 + cos x)^2

- so a = 1 and b = 2.