Question

find the derivative of the function Y=root x with respect to x by using first principles
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Answer 1

Answer:

dy/dx = 1/(2√x)

Step-by-step explanation:

find the derivative of the function Y=root x with respect to x by using first principles

y = √x

y + Δy = √(x + Δx)

y + Δy  - y = √(x + Δx) - √x

=> Δy = √(x + Δx) - √x

=> Δy = (√(x + Δx) - √x) * (√(x + Δx) + √x)/(√(x + Δx) + √x)

=> Δy = Δx/(√(x + Δx) + √x)

=> Δy/ Δx = 1/(√(x + Δx) + √x)

putting Δx = 0

dy/dx = 1/(√x + √x)

=> dy/dx = 1/(2√x)