Example 16 __
If s = e−t(sin t − cos t), find s′.
SOLUTION: s′ = e−t (cos t + sin t) + (sin t − cos t)(−e−t)
= e−t (2 cos t) = 2e−t cos t.Example 17 __
Let y = 2u^3 − 4u^2 + 5 u − 3 and u = x^2 − x. Find .
SOLUTION: = (6u^2 − 8u + 5)(2x − 1)
= [ 6( x^2 − x)^2 − 8( x^2 − x) + 5 ](2x − 1).Example 18 __
If y = sin (ax + b), with a and b constants, find .
SOLUTION: = [ cos(ax + b) ] · a = a cos(ax + b).
Example 19 __
If f (x) = aekx (with a and k constants), find f ′ and f ′′.
SOLUTION: f ′(x) = kaekx and f ′′ = k^2 aekx.