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Unformatted text preview: 3 L’HOPITAL’S RULE: If the limit of the quotient of differentiable functions f ( x ) and g ( x ) are of types 0 or ∞ , 0 ∞ = lim x→3 . ) x2 − 5 − 1 − x x2 − 9 ⎛ x2 − 5 + 1 + x ⎞ ⎜ ⎟ ⎝ ⎠ ( ( ) ) x2 − x − 6 x − 9 ⎛ x2 − 5 + 1 + x ⎞ ⎜ ⎟ ⎝ ⎠ 2 d (sec x ) = sec x ⋅ tan x , dx d (csc x ) = − csc x ⋅ cot x dx CHAIN RULE: f ( x ) = (a o b )( x ) , then f ′( x ) = a ′(b( x )) ⋅ b ′( x ) If More free Study Sheets and Practice Tests at: www.prep101.com More free study sheets and practice tests at Step 1. Take the ‘ln’ of both sides (to find an expression of the form ln y = ln[ f ( x )] ). EXAMPLE: Evaluate the derivative of the function y = tan sec e sin( x ) . (( )) SOLUTION: (( )) y ′ = sec 2 sec e sin ( x ) ⋅ (( d sec e sin ( x ) dx )) [ ( (( Step 2. Simplify )) )] )( )) [ ( )] )( y...
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