Question 54 of 70beginner🔧 ApplyShort Answer1 mark

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): sin⁡(x+a)\sin(x + a)

Correct Answer

cos(x + a)

Exercise: Miscellaneous Exercise on Chapter 12 | Q: 14 | (Page Page 37)
For More Understanding

Explanation

This is a 1-mark question asking for the derivative of sin(x + a). Using the chain rule of differentiation: d/dx[sin(x + a)] = cos(x + a) · d/dx(x + a) = cos(x + a) · 1 = cos(x + a). Alternatively, using expansion: sin(x + a) = sin x cos a + cos x sin a, and differentiating gives cos x cos a - sin x sin a = cos(x + a).

Solution Steps

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

  2. Step 2: Using chain rule: d/dx[sin(x + a)] = cos(x + a) · d/dx(x + a)

  3. Step 3: Since d/dx(x + a) = 1, we get d/dx[sin(x + a)] = cos(x + a)

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