Find the derivative of 99x at x = 100

Solution:

Let f (x) = 99x

The limit definition of a derivative is,

f' (100) = limₕ→₀ [f (100 + h) - f (100)]/h

= limₕ→₀ {[99 (100 + h)] - 99(100)}/h

= limₕ→₀ (9900 + 99h - 9900)/h

= limₕ→₀ (99h)/h

= limₕ→₀ (99)

= 99

Thus, the derivative of 99x at x = 100 is 99

NCERT Solutions Class 11 Maths Chapter 13 Exercise 13.2 Question 3

Find the derivative of 99x at x = 100

Summary:

Thus, the derivative of 99x at x = 100 is 99