Question:
Find the derivative of the following functions: (4x+5Sinx) /(3x+7C0sx)
Answer:
Let y = (4x+5Sinx) /(3x+7Cosx)
then dy/dx = {(3x + 7cosx)*(4 + 5cosx) - (4x + 5sinx)*(3 - 7sinx)}/(3x + 7sinx)2
= {(12x + 15x*cosx + 28cosx + 35cos2 x) - (12x - 28x*sinx + 15*sinx - 35sin2 x)}/(3x + 7sinx)2
= {12x + 15x*cosx + 28cosx + 35cos2 x - 12x + 28x*sinx - 15*sinx + 35sin2 x)}/(3x + 7sinx)2
= {15x*cosx + 28cosx + 28x*sinx -15sinx + 35(cos2 x + sin2 x)}/(3x + 7sinx)2
= {15x*cosx + 28cosx + 28x*sinx -15sinx + 35}/(3x + 7sinx)2 (since cos2 x + sin2 x = 1)
So derivative of (4x+5Sinx) /(3x+7Cosx) = {15x*cosx + 28cosx + 28x*sinx -15sinx + 35}/(3x + 7sinx)2
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