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

ncert cbse 11th limits and derivatives miscellaneous exercise

29.

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

y = (x+secx)(x-tanx)

using product formula for differentiation

y = uv

dy/dx = uv' +vu'

u =(x+secx)

v=(x-tanx)

taking derivative

u' = 1 + secxtanx

v' = 1 - [(secx)^2]

dy/dx = uv' +vu'

dy/dx =(x+secx) {1 - [(secx)^2]} +(x-tanx){1 + secxtanx ]

28.

find the derivative of x / (1+tanx)

using quotient formula for differentiation

y = u/v

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

u=x

v=(1+tanx)

taking derivative

u' = 1

v' = 0 + [(secx)^2] =[(secx)^2]

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

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

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

28.

find the derivative of x / (1+tanx)

solution

29.

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

solution

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