We have, sec (x+y)=xy On differentiating both sides w.r.t x, we get `sec (x+y)cdot tan (x+y) cdot (d)/(dx) (x+y) = x (dy)/(dx)+y` `rArr overset(cdot)sec (x+y) cdot tan (x+y) cdot (1+(dy)/(dx))=x(dy)/(dx)+y` `rArr (dy)/(dx)[sec (x+y)cdot tan (x+y)-x]` `=y-sec (x+y)cdot. tan (x+y)` `therefore (dy)/(dx)=(y-sec(x+y).tan (x+y))/(sec (x+y). tan (x+y)-x`
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
Solve by the method of elimination 3(2x+ y ) = 7xy , 3( x + 3y ) = 11xy
If cos ( xy) = x , show that (dy)/(dx) = -((1+ y sin (xy)))/(x sin xy)
By using properties of determinants , show that : {:[( x,x^(2) , yz) ,( y,y^(2) , zx ) ,( z , z^(2) , xy ) ]:} =( x-y)(y-z) (z-x) (xy+yz+ zx)
