Calculus Cheat Sheet Derivatives Definition and Notation f (x+ h) - f (x) If y = f (x) then the derivative is defined to be f' (x) = lim h+O h If y= f (x) then all of the following are f (x) all of the following are equivalent equivalent notations for the derivative. notations for derivative evaluated at x= a. fl(a) = ~/l~=~ =gl = 31 = of (a) dx ,a Interpretation of the Derivative If y = f (x) then, 2. fl(a) is the instantaneous rate of 1. m = f '(a) is the slope of the tangent change of f (x) at x= a. line to y= f (x) at x= aand the 3. If f (x) is the position of an object at equation of the tangent line at x= a is time x then f '(a) is the velocity of given by y = f (a) + f '(a) (x- a) . the object at x= a. Basic Properties and Formulas If f (x) and g(x) are differentiable functions (the derivative exists), c and n are any real numbers,
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