# derivatives 1

 what is the derivative of f(x) defined as? derivative of f(x) is provided the limit exists what are the two interpretations o derivative? 1. slope o tangent line o function at that point2. instantaneous rate o change o function at the point derivative is also what? a function* provided the limit exists when is function f(x) called differentiable? at x=a if limit f'(a) existsdifferentiable everywhere if f'(x) exists for all x what is the process of taking a derivative called? differentiation when is f(x) not differentiable? if f'(a) or f'(x) D.N.E. at x=a or all x values what is diff b/twn f'(a) and f'(x) f'(a) = numberf'(x) = function write prime notation, liebniz notation f'(x) how to find derivative of f(x) = x2 + 3 with limits? sub it into equation, use lim approaching h  constant function rule if f(x) = kf'(x) = 0includes values like pi, and other numbers power rule if f(x) = xnf'(x) = nxn-1 constant multiple rule if f(x) = kg(x), where k is set real numbers and g(x) differentiablef'(x) = kg'(x) proof for constant multiple rule product rule let u(x) and v(x) be differentiable(uv)'=u'v + uv'if u(x) and v(x)  and h(x) be differentiable(uvh)'=u'vh + uv'h + uvh' power of a function rule when factoring (3x2-2x)4 (3x2-2x)4=[x(3x-2)]4 =x4(3x-2)4 quotient rule if u(x) and v(x) are differentiable then what should you always do before trying to solve for a derivative? SIMPLIFYACA Authorkayekitty ID177471 Card Setderivatives 1 Descriptioncalculus derivatives 1 Updated2012-10-14T02:58:27Z Show Answers