find the derivative of {ax+b}/{cx+d}

ncert cbse 11th limits and derivatives miscellaneous exercise

5.find the derivative of {ax+b}/{cx+d}

using quotient rule of differentiation

if y = (u/v)

dy/dx = {vu' - uv'} / {v^2}

u = {ax+b}; v = {cx+d}

u ' = a ; v ' = b

dy/dx ={(cx+d)(a) -(ax+b)(c)} / {(cx+d)^2}

dy/dx = {ad-bc} / {(cx+d)^2}

2. find the derivative of {px+q}{(r/x)+s}

using product rule of differentiation

 

if y =uv

dy/dx = uv' +vu'

u =px+q ; v = {(r/x)+s}

u' = p(1)+0 = p  ; v ' = {{-r} / {x^2} + 0] = {-r} / {x^2}

y = {px+q}{(r/x)+s}

dy/dx = uv' +vu'

dy/dx = {px+q}{{-r} / {x^2}} +{(r/x)+s}{p}

dy/dx = {{-pr}/ {x} } -{{qr} / {x^2}} +{{rp}/x} +sp

dy/dx = -{{qr} / {x^2}} +ps

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

2. find the derivative of {px+q}{(r/x)+s}

solution

5.find the derivative of {ax+b}/{cx+d}

solution

7. find the derivative of {1} / {a x^2 + bx + c }

solution

8.find the derivative of {ax+b}/{p x^2+ qx +r}

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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