{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}


What is the glide ratio glide horizontal speed ut 600

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: n a capacitor, cur rent, voltage, resistance, energy, cost, population, time, probability, or any other quantity that CHANGES. The calculation to find the deriv tiv deri v a ti v e f ’ (x) , the expression of the INSTANTANEOUS RATE OF CHANGE, from the function f(x), the expression of CHANGE, is almost mechanical. Deriv tiv Below is a par tial Ta ble of Deri v a ti v es o f the more frequently encountered functions in standard form. function f(x) f (x) derivative f ’(x) xn (n is a rational number) n xn−1 ex ex log (x) 1/ x sin (x) cos (x) cos (x) − sin (x) tan (x) sec2 (x) cosec (x) − cosec (x). cot (x) . sec (x) sec (x) . tan (x) cot (x) − cosec2 (x) sin −1(x) √1 − x 2 1 − cos −1(x) 1 √1 − x 2 1 √1 +x 2 tan −1(x) 79 differentia We may differentiate various combinations of functions using the following rules. dif entiate Let u(x) and v(x) be functions of x, the independent variable. function derivative C (constant) 0 du C ----dx du dv --- ----- + --dx dx du dv --- ----- − --dx dx du dudv dv ---v u ---++uv--- -----dx dxdx dx dv du du--dv ---v u dx--−u v dx ------ --- dx dx C. u . u+v u−v u.v u /v v2 Chain r ule Let u(v) be a function of v and v(x) be a function of x, the independent variable. du(v) d dv(x) du(v) d = d . dx dv dx Higher order derivatives dy If y(x) is a function of x , then y’(x) = --- is also a function of x. If y’(x) is a --dx well-behaved function, then the derivative of y’(x) is : derivative dy’ d2y d dy --- = --- (--- ) = ----2 . --- -----y ” = --dx dx dx dx y ” is the second derivative of y(x) with respect to x. This is known as successive second successive n n−1 differentiation . In general : d y d dy ---------n = --- ( n−1 ) dx dx dx 80 Example : y(t) is the function that expresses CHANGE in height. y ’ (t) is the INSTANTANEOUS RATE OF CHANGE in height or ver tical speed. We can think of y ’ (t) as the function that expresses CHANGE in ver tical speed and y ”(t) the INSTANTANEOUS RATE OF CHANGE in ver tical s...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online