Calculus

Calculus Cheat canvass Calculus Cheat Sheet derived functions Definition and eminence f ( x + h) - f ( x) If y = f ( x ) then the derivative is defined to be f ¢ ( x ) = lim . h ®0 h If y = f ( x ) then any of the succeeding(a) are homogeneous notations for the derivative. df dy d f ¢ ( x ) = y¢ = = = ( f ( x ) ) = Df ( x ) dx dx dx If y = f ( x ) all of the following are equivalent notations for derivative evaluated at x = a . df dy f ¢ ( a ) = y¢ x =a = = = Df ( a ) dx x= a dx x=a Chain hold Variants The chain rule applied to rough specific functions. n n -1 d d é f ( x ) ù = n é f ( x )ù f ¢ ( x ) 1. 5. cos lettuce é f ( x ) ù = - f ¢ ( x ) intrude é f ( x ) ù û ë û ë û ë û dx ë dx d d f ( x) f x 2. burn mark é f ( x ) ù = f ¢ ( x ) sec2 é f ( x ) ù e = f ¢( x ) e ( ) 6. ë û ë û dx dx d f ¢( x) d 7. ( sec [ f ( x )]) = f ¢( x ) sec[ f ( x)] tan [ f ( x )] ln é f ( x ) ù = 3. ë û dx dx f ( x) f ¢( x) d d 8. tan-1 é f ( x ) ù = 4. sin é f ( x ) ù = f ¢ ( x ) cos é f ( x ) ù 2 ë û ë û ë û dx 1 + é f ( x)ù dx ë û ( ) ( ( ( ) ( ) ) ( ( ) ) ) If y = f ( x ) then, interpretation of the differential 2. f ¢ ( a ) is the instantaneous rate of depart of f ( x ) at x = a . 3.

If f ( x ) is the position of an aspiration at time x then f ¢ ( a ) is the velocity of the object at x = a . 1. m = f ¢ ( a ) is the set up of the tangent line to y = f ( x ) at x = a and the equality of the tangent line at x = a is wedded by y = f ( a ) + f ¢ ( a )( x - a ) . high Order Derivatives The Seco nd Derivative is denoted as The nth Derivati! ve is denoted as 2 d f dn f f ¢¢ ( x ) = f ( 2) ( x ) = 2 and is defined as f ( n ) ( x ) = n and is defined as dx dx ¢ , i.e. the derivative of the ¢ (n) f ¢¢ ( x ) = ( f ¢ ( x ) ) f ( x ) = f ( n -1) ( x ) , i.e. the derivative of outset derivative, f ¢ ( x ) . the (n-1)st derivative, f ( n -1) x . ( ) rudimentary Properties and Formulas If f ( x ) and g ( x ) are differentiable functions (the derivative exists), c and n are any real...If you destiny to get a honorable essay, order it on our website: OrderCustomPaper.com

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