Home
Class 12
MATHS
Find (dy)/(dx) for the function: y=(log)...

Find `(dy)/(dx)` for the function: `y=(log)_esqrt((1+sinx)/(1-sinx)),where x=pi/3`

Text Solution

Verified by Experts

The correct Answer is:
2
`y=log sqrt((1+ sin x)/(1- sin x))=(1)/(2)[log_(e)(1+ sin x) -log _(e) (1- sin x)]`
`therefore" "(dy)/(dx)=(1)/(2){(1)/(1+ sin x dx)(d)/(dx)(1+ sin x)-(1)/(1- sin x )(d)/(dx)(1- sin x )}`
`=(1)/(2){(cos x)/(1+ sin x)+(cos x )/(1-sin x)}`
`=(1)/(2)cos x ((2)/(1- sin^(2)x))=(cos x)/(cos^(2)x)=sec x`
`"or "(dy)/(dx):|_(x=(pi)/(3))=sec""(pi)/(3)=2`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Concept Application 3.3|10 Videos

  • DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Concept Application 3.4|12 Videos

  • DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Concept Application 3.1|1 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|578 Videos

  • DOT PRODUCT

    CENGAGE PUBLICATION|Exercise DPP 2.1|15 Videos

Similar Questions

Explore conceptually related problems

Find (dy)/(dx) for the function: y= sin x + ln x

Find (dy)/(dx) for the functions: y=(x+sinx)/(x+cosx)

Find (dy)/(dx) for the functions: y=(x+sinx)/(x+cosx)

Show that (dy)/(dx)=sec x . If y=(log)sqrt((1+sinx)/(1-sinx))

Find (dy)/(dx) when : y=log sqrt((1+sinx)/(1-sinx))

find int(dx)/(1+sinx)

Find (dy)/(dx) , when y=(sinx)/(logx)

Find (dy)/(dx) , when y^(2)=(sinx)^(-x)

Find (dy)/(dx) when : x^(sin y)+y^(sinx)=1

sinx(dy)/(dx)+y=y^(2)