Question 43 of 70beginner🔧 ApplyShort Answer1 mark

Find the derivative of the following functions (it is to be understood that a,b,c,d,p,q,ra, b, c, d, p, q, r and ss are fixed non-zero constants and mm and nn are integers):

(x+a)(x + a)

Correct Answer

1

Exercise: Miscellaneous Exercise on Chapter 12 | Q: 2 | (Page Page 37)
For More Understanding

Explanation

The question asks for the derivative of (x + a), where a is a fixed non-zero constant. Using the sum rule of derivatives, the derivative of a sum is the sum of derivatives. The derivative of x with respect to x is 1 (using the standard derivative formula d/dx(xnx^{n}) = nx^(n-1) with n=1), and the derivative of any constant a is 0. Therefore, the derivative of (x + a) is 1 + 0 = 1.

Solution Steps

  1. Step 1: Let f(x) = x + a

  2. Step 2: Using the sum rule: d/dx(x + a) = d/dx(x) + d/dx(a)

  3. Step 3: Using d/dx(xnx^{n}) = nx^(n-1), we get d/dx(x) = 1·x0x^{0} = 1

  4. Step 4: Since a is a constant, d/dx(a) = 0

  5. Step 5: Therefore, d/dx(x + a) = 1 + 0 = 1

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