Derivative from the Definition
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Tap a term to see what it means, or .
Calculate
Example: the slope of y = x² at x = 1 is exactly 2. With a step h = 0.1, what does the secant give? Change the function, the point and the step to work out your own case.
Step by step
What each term means
- Derivative (f′(x))
- The instantaneous rate of change of f at x: the slope of the tangent line to the curve there.
- Limit (h → 0)
- The value the quotient approaches as the step h shrinks to zero. At exactly h = 0 the calculation would be 0/0; the limit gets around that.
- Change in f (f(x + h) − f(x))
- How much the function changes when moving h away from x: the vertical side of the triangle under the secant.
- Step (h)
- How far to move in x. Dividing the change in f by h gives the slope of the secant, the line through (x, f(x)) and (x + h, f(x + h)).