What is the formula for the derivative at a point?
f(a+h)-f(a)/h
The formula for the derivative at a point is:
f ‘(a) = lim(x -> a) [f(x) – f(a)] / (x – a)
where f(x) is the function and ‘a’ is the point at which we want to find the derivative.
This formula shows the rate of change of the function f(x) at the point ‘a’. We take the limit of the difference quotient as x approaches ‘a’ to find the tangent line to the curve at that point. The derivative at ‘a’ gives the slope of the tangent line to the curve at that point.
Alternatively, we can also use the definition of the derivative as:
f ‘(a) = lim(h -> 0) [f(a + h) – f(a)] / h
where ‘h’ is a small increment in the x-axis. This definition represents the slope of the line that passes through the point (a, f(a)) and (a+h, f(a+h)), and we take the limit as h approaches 0.
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