Home
Class 12
MATHS
Prove that (d^n)/(dx^n)(e^(2x)+e^(-2x))=...

Prove that `(d^n)/(dx^n)(e^(2x)+e^(-2x))=2^n[e^(2x)+(-1)^n e^(-2x)]`

Text Solution

Verified by Experts

`(d)/(dx)[e^(2x)+e^(-2x)]=2e^(2x)-2e^(-2x)=2^(1)[e^(2x)-e^(-2x)]`
`(d)/(dx^(2))(e^(2x)+e^(-2x))=(d)/(dx)(e^(2x)-e^(-2x))=2^(2)(e^(2x)+e^(-2x))`
`(d^(3))/(dx^(3))(e^(2x)-e^(-2x))=(d)/(dx)2^(2)(e^(2x)+e^(-2x))=2^(3)(e^(2x)-e^(-2x))`
`because" "(d^(n))/(dx^(n))[e^(2x)+e^(-2x)]=2^(n)[e^(2x)+(-1)^(n)e^(-2x)]`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise 3.9|14 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise (Single)|137 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise 3.7|6 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Question Bank|7 Videos

  • DOT PRODUCT

    CENGAGE|Exercise DPP 2.1|15 Videos

Similar Questions

Explore conceptually related problems

int(e^x)/(e^(2x)+4)dx

(dy)/(dx) = e^(2x-y) + x^(3) e^(-y)

Evaluate int(dx)/(sqrt(1+e^(x)+e^(2x)))

Integrate the functions (e^(2x)-e^(-2x))/(e^(2x)+e^(-2x))

int_(0)^(1)e^(2x)e^(e^(x) dx =)

Show that int_(0)^(1)(e^(x))/(1+e^(2x))dx=tan^(-1)(e)-pi/(4)

Integrate (e^(2x) + e^(-2x) + 2)/(e^x)

If y=sqrt((1+e^(x))/(1-e^(x))) , show that (dy)/(dx)=e^(x)/((1-e^(x))sqrt(1-e^(2x))) .

Evaluate: int(e^x)/(e^(2x)+6e^x+5)dx

Answer the equation: int(e^((x)/(2))-e^(-(x)/(2)))/(e^(x)-e^(-x))dx