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50 POINTS !!!!! HomeWorker Helperer please1) Using the quotient rule, find [tex]y = \frac{cosx - s...
4 months ago
Q:
50 POINTS !!!!! HomeWorker Helperer please1) Using the quotient rule, find [tex]y = \frac{cosx - sinx}{cosx + sinx}[/tex]2) Given that [tex]y = \frac{x-1}{x+1}[/tex] , prove that [tex](x+1)(\frac{d^{2}y }{dx^{2} }) + 2(\frac{dy}{dx}) = 0[/tex]
Accepted Solution
A:
Answer:1) - 2 / (cos x + sinx)^2.Step-by-step explanation:1) I assume you want the derivative of (cos x - sin x) / ( cos x + sin x).y' = (cosx + sinx)( -sinx - cosx) - (cosx - sinx)(-sinx + cosx) --------------------------------------------------------------------------- (cosx + sinx)^2= -sinxcosx - cos^2x - sin^2x - sinxcosx - (-sinxcosx+cos^2x+sin^2x-sinxcosx ------------------------------------------------------------------------------------------------------- (cosx + sinx)^2= -2sinxcosx - 1 - ( -2sinxcosx + 1 ) / (cosx + sinx)^2= -2sinxcosx - 1 - ( -2sinxcosx + 1 ) / (cosx + sinx)^2 = - 2 / (cos x + sinx)^2.