Find the derivative of x² - 2 at x = 10

Solution:

Let f (x) = x² - 2

The limit definition of a derivative is,

f' (10) = limₕ→₀ [f (10 + h) - f (10)]/h

= limₕ→₀ {[(10 + h)² - 2] - (10² - 2)} / h

= limₕ→₀ (10² + 2.10.h + h² - 2 - 10² + 2)/h

= limₕ→₀ (20h + h²)/h

= limₕ→₀ (20 + h)

= 20 + 0

= 20

Thus, the derivative of x² - 2 at x = 10 is 20

NCERT Solutions Class 11 Maths Chapter 13 Exercise 13.2 Question 1

Find the derivative of x² - 2 at x = 10

Summary:

The value of the derivative of x² - 2 at x = 10 is 20