fourth,fifth and higherderivativesof f. Theyare denotedby f ', f ", f '", f(4), f(5),...
Example10:
Find the fifth derivativeoff(x) = 2x^4 - 3x^3 + 5x^2 - x- 1.
Solution:
Example11:
Showthat satisfiesthe differentialequation
Solution:
We needto obtainthe first, second,and third derivativesand substitutetheminto the differentialequation.
Substituting,
whichsatisfiesthe equation.
ReviewQuestions
Use the resultsof this sectionto find the derivativesdy/dx.
1.y= 5x^7
y =
(wherea,bare constants)