Tamil Nadu Board of Secondary EducationHSC Arts Class 11

# Find the derivatives of the following functions using first principle. f(x) = – 4x + 7 - Mathematics

Sum

Find the derivatives of the following functions using first principle.

f(x) = – 4x + 7

#### Solution

f(x + Δx) = – 4(x + Δx) + 7

f(x + Δx) – f(x) = [– 4(x + Δx) + 7] – [– 4x + 7]

f(x + Δx) – f(x) = [– 4(x + Δx) + 7] + 4x – 7

f(x + Δx) – f(x) = – 4 Δx

(f(x + Deltax) - f(x))/(Deltax) = - 4 (Deltax)/(Deltax)

lim_(Deltax -> 0) (f(x + Deltax) - f(x))/(Deltax) = lim_(Deltax -> 0) - 4

f"'"(x) = – 4

Concept: Differentiability and Continuity
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Chapter 10: Differential Calculus - Differentiability and Methods of Differentiation - Exercise 10.1 [Page 147]

#### APPEARS IN

Tamil Nadu Board Samacheer Kalvi Class 11th Mathematics Volume 1 and 2 Answers Guide
Chapter 10 Differential Calculus - Differentiability and Methods of Differentiation
Exercise 10.1 | Q 1. (ii) | Page 147
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