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

ncert cbse 11th limits and derivatives miscellaneous exercise

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

y=[(x^2)+1][cosx]

using product rule of differentiation

y = uv

dy/dx = uv' +vu'

u =[(x^2)+1]

v=cosx

u ' =2x+0 = 2x

v ' = (-sinx)

dy/dx = uv' +vu'

dy/dx = [(x^2)+1](-sinx)) +[cosx][2x]

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

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

y=[a(x^2)+sinx ] [p+qcosx]

using product rule of differentiation

y = uv

dy/dx = uv' +vu'

u =[a(x^2)+sinx ]

v =[p+qcosx]

u ' = a(2x)+cosx = 2ax+cosx

v ' =0 - qsinx

dy/dx = uv' +vu'

dy/dx = [a(x^2)+sinx ][ - qsinx] + [p+qcosx][ 2ax+cosx]

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

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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