Question

3. Find the derivative of root x with respect to x.​

Answer 1

Given:

f(x) = √x

To find:

The derivative of √x with respect to x.​

Solution:

f(x) = √x = x^(¹/₂)

d/dx(xⁿ) = nx⁽ⁿ ⁻ ¹⁾

d/dx(√x) = 1/2 x^(¹/₂ - 1)

d/dx(√x) = 1/2 x^(-¹/₂)

d/dx(√x) = 1/(2√x)

So, the derivative of √x with respect to x is 1/(2√x).

Questions for practice:

Q1: f(x) = x³ + 5x² + 45

Q2: y = 26a where a = constant

Q3: y = (1 + x³)(12x + x²)