Home
Class 12
MATHS
Find (dy)/(dx) for y=sin^(-1)(cosx), whe...

Find `(dy)/(dx)` for `y=sin^(-1)(cosx),` where `x in (0,2pi)dot`

Text Solution

Verified by Experts

We have,
`sin^(-1)(cos x)=(pi)/(2)-cos^(-1)(cos x)`
`={:{((pi)/(2)-"x,"," "if 0ltxltpi),((pi)/(2)-(2pi-x)","," "if piltxlt2pi):}`
`={:{((pi)/(2)-"x,"," "if 0ltxltpi),(x-(3pi)/(2)-(2pi-x)","," "if piltxlt2pi):}`
`therefore" "(d)/(dx){sin^(-1)(cos x)}={:{(-1","," "if 0ltxltpi),(1","," "if piltxlt2pi):}`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise 3.1|7 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise 3.2|38 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Question Bank|7 Videos

  • DOT PRODUCT

    CENGAGE|Exercise DPP 2.1|15 Videos

Similar Questions

Explore conceptually related problems

Find (dy)/(dx) for y=sin(x^2+1)dot

Which of the following is/are true? (dy)/(dx)fory=sin^(-1)(cosx),w h e r ex in (0,pi),i s-1 (dy)/(dx)fory=sin^(-1)(cosx),w h e r ex in (0,2pi),i s1 (dy)/(dx)fory=cos^(-1)(sinx),w h e r ex in (-pi/2,pi/2),i s-1 (dy)/(dx)fory=cos^(-1)(sinx),w h e r ex in (pi/2,(3pi)/2),i s-1

Find (dy)/(dx) where y=(tanx)/(x)

Find (dy)/(dx) if y =e^(x) sin 2x

Find (dy)/(dx)" if "x-y = pi .

Find dy/dx if y = sin x^(@)

Find (dy)/(dx)," if "y+ sin y= cos x .

Find (dy)/(dx) for y=tan^(-1){(1-cosx)/(sinx)},-piltxltpi

find dy/dx if y = (logx)^(sin^(-1)x