Question 31 of 70beginner🔧 ApplyNumerical1 mark

Find the derivative of x2−2x^2 - 2 at x=10x = 10.

Correct Answer

20

Exercise: EXERCISE 12.2 | Q: 1 | (Page Page 32)
For More Understanding

Explanation

This question is from Exercise 12.2 of the NCERT textbook. The solution requires finding the derivative of the function f(x) = x² - 2 and then evaluating it at x = 10. Using Theorem 6 from the context, the derivative of xnx^{n} is nx^(n-1). For x², this gives 2x. For the constant term -2, Example 11 shows that the derivative of any constant function is 0. Therefore, the derivative of x² - 2 is 2x, and at x = 10, the value is 2(10) = 20.

Solution Steps

  1. Step 1: Let f(x) = x² - 2. We need to find f'(x) first.

  2. Step 2: Using Theorem 6, derivative of x² = 2x^(2-1) = 2x.

  3. Step 3: Using Example 11, derivative of constant -2 is 0.

  4. Step 4: Therefore, f'(x) = 2x + 0 = 2x.

  5. Step 5: At x = 10, f'(10) = 2(10) = 20.

PreviousNext