find the derivative of (sinx+cosx)/(sinx-cosx)

ncert cbse 11th limits and derivatives miscellaneous exercise

17.find the derivative of (sinx+cosx) / (sinx-cosx)

using quotient rule for differentiation

if y = (u/v)

dy/dx = [vu' - uv'] / [v^2]

u = sinx + cosx

v = sinx -  cosx

u' = cosx - sinx

v' = cosx + sinx

y = (sinx+cosx)/sinx-cosx)

dy/dx ={(sinx-cosx)(cosx - sinx) -(sinx+cosx)(cosx + sinx)}/{(sinx-cosx)^2}

on simplification

dy/dx = -2{(sinx)^2 + (cosx)^2} / {(sinx-cosx)^2}

using trigonometry formula trigonometry identities

{(sinx)^2 + (cosx)^2} = 1

dy/dx = (-2) / {(sinx-cosx)^2}

18. find the derivative of (secx -1) / (secx+1)

using quotient rule for differentiation

if y = (u/v)

dy/dx = [vu' - uv'] / [v^2]

u = (secx -1)

v = (secx + 1)

u' = secx tanx

v' = secx tanx

y =(secx -1) / (secx+1)

dy/dx = [vu' - uv'] / [v^2]

dy/dx = [(secx +1)(secx tanx) - (secx -1)(secx tanx) ] / [(secx + 1)^2]

on simplification

dy/dx = [2secx tanx] / [(secx + 1)^2]

13. limits and derivatives
miscellaneous exercise

1.

(i)  find the derivative of (-x) using first principles
solution

(ii)   find the derivative of [ (-x)^(-1) ] using first principles

solution

(iii)find the derivative of sin(x+1) using first principles

solution

(iv) find the derivative of cos[x-(pi/8)] using first principles
solution

17.find the derivative of (sinx+cosx) / (sinx-cosx)

solution

18. find the derivative of (secx -1) / (secx+1)

solution

23.find the derivative of [(x^2)+1][cosx]

solution

24. find the derivative  of (a(x^2)+sinx )[p+qcosx]

solution

28.

find the derivative of x / (1+tanx)

solution

29.

find the derivative of (x+secx)(x-tanx)

solution

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