Question

Differentiate the following function from the first principal :

sin^–1(2x + 3)

Answer 1

We have to find the derivative of sin^–1(2x+3) with the first principle method, so,

f(x) = sin^–1(2x+3)

by using the first principle formula, we get,

Let sin^–1[2(x+h)+3] = A and sin^–1(2x+3) = B, so,

sinA = [2(x+h)+3] and sinB = (2x+3),

2h = sinA – sinB, when h→0 then sinA→sinB we can also say that A→B and hence A–B→0,

[By using Pythagoras theorem, in which H = 1 and P = 2x+3, so, we have to find B, which comes out to be\(\sqrt{1-(2x+3)^2}\) by the relation H² = P² + B²]