Transcription of MATHEMATICS FOR ENGINEERING DIFFERENTIATION TUTORIAL 2 ...
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MATHEMATICS FOR ENGINEERING DIFFERENTIATION TUTORIAL 2 ...
MATHEMATICS FOR ENGINEERING DIFFERENTIATION TUTORIAL 2 advanced DIFFERENTIATION CONTENTS Function of a Function DIFFERENTIATION of a Sum DIFFERENTIATION of a Product DIFFERENTIATION of a Quotient Turning Points In this TUTORIAL you will learn how to differentiate more complicated expressions. Below is a list of standard differentials. kxkx121nnakedxdy aeyx1xdxdy ln(ax)yatan(ax)adxdy tan(ax)yasin(ax)dxdy cos(ax)yacos(ax)dxdy sin(ax)yanxdxdy axy=====+== ====== 1 1. FUNCTION OF A FUNCTION If a variable y depends on a second variable u which in turn depends on a third variable x, then dxdududydxdy=and this is the chain rule. If we have y = f(u) and u = f (x) then we find that: (x)f (u)fdxdy = dxdu (x)f and dudy (u)f= = Put another way, we can substitute a function into another function to simplify the DIFFERENTIATION process.
MATHEMATICS FOR ENGINEERING DIFFERENTIATION TUTORIAL 2 – ADVANCED DIFFERENTIATION CONTENTS • Function of a Function • Differentiation of a Sum • Differentiation of a Product • Differentiation of a Quotient • Turning Points In this tutorial you will learn how to differentiate more complicated expressions. Below is a list of
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