Home
Class 12
MATHS
Find the derivative of the function give...

Find the derivative of the function given by `f(x)=(1+x)(1+x^2)(1+x^4)(1+x^8)` and, hence, find `f^(prime)(1)dot`

Text Solution

Verified by Experts

`f(x) = (1+x)(1+x^(2))(1+x^(4))(1+x^(8))`
`rArr "log"f(x) = "log"(1+x) + "log" (1+x^(2)) + "log"(1+x^(4)) + "log"(1+x^(8))`
Differentiate both side w.r.t.x
`(f'(x))/(f(x)) = (1)/(1+x) + (2x)/(1+x^(2)) + (4x^(3))/(1+x^(4)) + (8x^(7))/(1+x^(8))`
`rArr f'(x)= f(x)[(1)/(1+x) + (2x)/(1+x^(2)) + (4x^(3))/(1+x^(4)) + (8x^(7))/(1+x^(8))]`
`rArr f'(x)= (1+x) (1+x^(2)) (1+x^(4)) (1+x^(8)) [(1)/(1+x) + (2x)/(1+x^(2)) + (4x^(3))/(1+x^(4)) + (8x^(7))/(1+x^(8))]`
`therefore f'(1) = (2)(2)(2)(2)[(1)/(2) + (2)/(2) + (4)/(2) + (8)/(2)]`
`= 16 ((1)/(2) + 1 + 2 + 4) = 120`
Promotional Banner

Topper's Solved these Questions

  • Continuity and Differentiability

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercies 5.6|11 Videos

  • Continuity and Differentiability

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercies 5.7|17 Videos

  • Continuity and Differentiability

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercies 5.4|10 Videos

  • APPLICATIONS OF INTEGRALS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|19 Videos

  • DETERMINANTS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|19 Videos

Similar Questions

Explore conceptually related problems

Find the derivative of the function f(x) given by f(x)=(1+x)(1+x^2)(1+x^4)(1+x^8) and hence find f^(prime)(1)

Find the derivative of f(x) =1/x

Find an anti-derivative of the function f(x)=1/x

Find the range of the function f(x)=((1+x+x^2)(1+x^4))/x^3

Find the derivative for function f(x)=x+1/x with respect to x

Find the derivative for function f(x)=x(x-1) with respect to x

Find the derivative of f(x) =(x+1)/x .

Find the domain of the function f(x)=(1)/(8{x}^(2)-6{x}+1).

Find the derivative for function f(x)=(x-1)(x-2)(x-3) with respect to x

Find the derivative of / given by f(x)=tan^(-1)x assuming it exists.