Limits and Derivatives

Limits and Derivatives

Question

For some constants a and b, find the derivatives of the following functions :

(ax+b)

Answer

y = (ax2 +b)

rightwards double arrow    space space space space space space space space space space straight y space equals space space straight a squared straight x to the power of 4 plus 2 abx squared plus straight b squared


rightwards double arrow          space space space space space space space space space space space space space space space space space dy over dx equals straight d over dx left parenthesis straight a squared straight x to the power of 4 right parenthesis plus straight d over dx left parenthesis 2 ab space straight x squared right parenthesis plus straight d over dx left parenthesis straight b squared right parenthesis equals straight a squared straight d over dx straight x to the power of 4 plus 2 ab straight d over dx straight x squared plus 0

             space space space space space space space space space space space space space space equals space space straight a squared straight x space 4 straight x cubed plus 2 abx 2 straight x equals 4 straight a squared straight x cubed plus 4 abx

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