Home
Class 12
MATHS
Find (dy)/(dx) if, y=(e^(a x) \ secx \ l...

Find `(dy)/(dx)` if, `y=(e^(a x) \ secx \ logx)/(sqrt(1-2x))`

Text Solution

Verified by Experts

Given that,
`y=(e^(a x) \ secx \ logx)/(sqrt(1-2x))`
`=>logy=log[(e^(a x) \ secx \ logx)/(sqrt(1-2x))]`
`=>logy=log(e^(ax))+log(secx)+log(logx)-log(1-2x)^(1/2)`
`=>logy=ax +log(secx)-1/2 log(1-2x)`
`=>1/y(dy)/(dx)=a+(secx*tanx)/(secx)+1/logx *1/x -1/2 (-2/(1-2x))`
`=>(dy)/(dx)=y[a+tanx+1/(xtanx)+1/(1-2x)]`
`=>(dy)/(dx)=(e^(a x) \ secx \ logx)/(sqrt(1-2x))[a+tanx+1/(xtanx)+1/(1-2x)]`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIALS, ERRORS AND APPROXIMATIONS

    RD SHARMA|Exercise Solved Examples And Exercises|102 Videos

  • DIRECTION COSINES AND DIRECTION RATIOS

    RD SHARMA|Exercise Solved Examples And Exercises|67 Videos

Similar Questions

Explore conceptually related problems

Find (dy)/(dx) , when: y=(logx)^(x)

Find (dy)/(dx) , when: y=(e^(x)logx)/(x^(2))

Find (dy)/(dx), if y=sin^(-1)[x sqrt(1-x)-sqrt(x)sqrt(1-x^(2))]

Find (dy)/(dx) of y=e^((x^(2))/(1+x^(2)))

x (dy)/(dx) - y = 2x ^(2) secx

Find (dy)/(dx) , if x =e^(m), y = e^(sqrt(m))

x (dy)/(dx) + y = x logx

Find (dy)/(dx) in the following: y=sin^(-1)(2x sqrt(1-x^(2))),-(1)/(sqrt(2))