Home
Class 12
MATHS
If (cosx)^y=(cosy)^x find (dy)/(dx) ....

If `(cosx)^y=(cosy)^x` find `(dy)/(dx)` .

Text Solution

Verified by Experts

`("cos" x)^(y) = ("cos" y)^(x)`
`rArr "log" ("cos" x)^(y) = "log" ("cos" y)^(x)`
`rArr y"log cos" x = x"log cos"y`
Differentiate both sides w.r.t.x
`y * (d)/(dx) "log cos"x + "log cos"x (d)/(dx)y`
`= x (d)/(dx)"log cos"y + "log cos"y(d)/(dx) x`
`rArr y * ((-"sin"x))/("cos"x) + "log cos"x * (dy)/(dx)`
`=(x(-"sin"y))/("cos"y)(dy)/(dx) + "log cos"y * 1`
`rArr -y"tan"x + "log cos"x (dy)/(dx)`
`= -x"tan"y (dy)/(dx) + "log cos"y`
`rArr ("log cos" x + x"tan"y)(dy)/(dx) = "log cos" y + y"tan"x`
`rArr (dy)/(dx) = ("log cos"y + y"tan"x)/("log cos"x + x"tan"y)`
Promotional Banner

Topper's Solved these Questions

  • Continuity and Differentiability

    NAGEEN PRAKASHAN|Exercise Exercies 5.6|11 Videos

  • Continuity and Differentiability

    NAGEEN PRAKASHAN|Exercise Exercies 5.7|17 Videos

  • Continuity and Differentiability

    NAGEEN PRAKASHAN|Exercise Exercies 5.4|10 Videos

  • APPLICATIONS OF INTEGRALS

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|19 Videos

  • DETERMINANTS

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|19 Videos

Similar Questions

Explore conceptually related problems

If y=(x)^(cosx)+(cosx)^(sinx) , find (dy)/(dx).

If x^(y)=y^(x), find (dy)/(dx)

If (cosx)^(y)=(siny)^(x), then find (dy)/(dx) .

x^(y)=y^(x) then find (dy)/(dx)

If y=x^cosx then find (dy)/(dx)

If y=sin(cosx^(2)), find (dy)/(dx) .

If y=(cosx)^((cosx)) then (dy)/(dx) is equal to :

If y=(sinx)/(x+cosx) , then find (dy)/(dx) .

If y = sin sqrt(cosx),"find"(dy)/(dx).

Find derivative of given functions w.r.t the respective independent variable . y=(cosx)/(x)+x/(cosx) Find (dy)/(dx) as a function of x