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Find derivative of the following functio...

Find derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): `(a+bsinx)/(c+dcosx)`

Text Solution

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Let `y=(a+bsinx)/(c+dcosx)`
`therefore (dy)/(dx) = ((c+dcosx)d/(dx)(a+bsinx)-(a+bsinx)d/(dx)(c+dcosx))/(c+d cosx)^(2)` ["by quotinet rule"]
`=((c+dcosx)(bcosx)-(a+bsinx)-(-dsinx))/(c+dcosx)^(2)`
`=((bc cosx+adsinx+bd(cos^(2)x+sin^(2)x))/(c+dcosx)^(2))`
`(bc cosx + adsinx+bd)/(c+dcosx)^(2)`
`(bccosx+adsinx+bd)/(c+dcosx)^(2)`
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