स्पर्श रेखा का ढलान कैलकुलेटर — सूत्र

Slope of a Tangent Line

Method

For f(x) = ax^n, the tangent line at x₀ has:

1. Slope = f'(x₀) = a × n × x₀^(n-1) 2. Point = (x₀, f(x₀)) 3. Tangent line equation: y - y₀ = m(x - x₀)

or equivalently: y = mx + (y₀ - mx₀)

हल किया गया उदाहरण

Find the tangent line to y = x² at x = 3.

  1. f(3) = 3² = 9, so the point is (3, 9)
  2. f'(x) = 2x, so f'(3) = 6
  3. Tangent line: y - 9 = 6(x - 3)
  4. y = 6x - 9