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This page is meant to serve as a quick overview of the basics of derivitives.
Derivitives
The derivative of a function is f'(x) = lim as h approaches 0 (f(x+h)f(x/h)), provided that the limit exist.
Alternative Approach
f'(a) = lim x ⇒ a ( f(x)  F(a) ) / (xa)
Differentiability
For any acute angle Θ in standard position, the following applies:
A corner  
A cusp  
A verticle tangent  
A discontinuity 
Derivative Rules
Derivative of a Constant  If c is a real number, the derivative of a constant function is 0.  d/dx[c] = 0 
Sum and Difference Rules  The sum or difference of any two differentiable functions is differentiable and is the sum or difference of their derivatives.  d/dx[f(x) + g(x)] = f'(x) + g'(x)
d/dx[f(x)  g(x)] = f'(x)  g'(x) 
Constant Multiple Rule  If f is a differentiable function and c is a constant, then cf is also differentiable  d/dx[cf(x)] = cf'(x) 
Power Rule  If n is a rational number, then the function f(x) = x^{n} is differentiable.  d/dx[x^{n}] = nx^{n1} 
Product Rule  The product of two differentiable functions, f and g, is differentiable.  d/dx[f(x)g(x)] = f(x)g'(x) + g(x)f'(x) 
Quotient Rule  The quotient f/g, of two differentiable functions, f and g, is differentiable at all values of x for which g(x) ≠ 0.  d/dx[ f(x)/g(x) ] = (g(x)f'(x)  f(x)g'(x)) / [g(x)]^{2} 
Chain Rule  No Explanation Currently  d/dx[f(g(x))] = f'(g(x))g'(x) 
Power Rule  If c is a real number, the derivative of a constant function is 0.  d/dx[f(g(x))] = f'(g(x))g'(x) 
Derivatives of Trig Functions
d/dx[sinx] = cosx  d/dx[cosx] = sinx  d/dx[tanx] = sec^{2}x 
d/dx[cscx] = csc x cot x  d/dx[secx] = sec x tan x  d/dx[cotx] = csc^{2}x 
Jerk
Jerk is the derivative of acceleration. Jt = da/dt = d^{3}s / dt^{3}
Implicit Differentiation
Used to find dy/dx when it is hard to find what y equals.
Inverse Trigonometric







