BSCE11 Lecture Notes - Differentiable Function, Power Rule, Quotient Rule
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Math1010u: chapter 3 1differentiation rules derivatives of polynomials and exponential functions(3. 1,p173) recall: last day, we learned how to find the derivative from first principles. Now, let"s consider some useful rules to help us do differentiation. Exponential function recall: earlier in the course, we introduced the exponential function. So, xafxf =)0(")(" in other words, the rate of change is proportional to the function itself. Definition: e is the number such that 11lim0= hehh the derivative of the natural exponential function, xe, is then given by: xxeedxd=)( example: find the derivative of xexfx173)(+=. Math1010u: chapter 3 3the product and quotient rules (section 3. 2, pg. 183) recall: we already know how to find the derivative of a sum or difference of functions. Math1010u: chapter 3 4derivatives of trigonometric functions (section 3. 3, pg. Let"s check first, we"ll need to know the following 2 limits: 1sinlim0= 01coslim0= and now, we proceed using the definition of a derivative (first principles):
