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Calculus Review: Polynomial Derivatives, Exponential & Trigonometric Functions

This review covers Polynomial Derivatives, Exponential Functions, Chain Rule, Product Rule, Trigonometric Functions, and Applications of Chain Rule in Calculus. Practice problems and concepts like Differentiating, Integrating Polynomials, and Trigonometric Functions are included.

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Calculus Review: Polynomial Derivatives, Exponential & Trigonometric Functions

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  1. Winter wk 6 – Tues.8.Feb.05 • Calculus Ch.3 review: • Polynomial rule for derivatives • Differentiating exponential functions • Chain rule and product rule • 3.5 Trigonometric functions • 3. 6 Applications of chain rule Energy Systems, EJZ

  2. Differentiating polynomials and ex Differentiating polynomials: Integrating polynomials: Slope of ex increases exponentially: d/dx(ex) = ex d/dx(ax) = ln(a) ax

  3. Review chain rule Differentiate exponential function y=eax Differentiate y=ex2=ez z=x2

  4. Review product rule and quotient rule If y(x) = f(x) g(x) then Practice: y = x2 e-3x =f.g where f=______, g=______ If y(x) = f(x) / g(x) then

  5. Differentiating trig functions Sketch the slope of y=sin(x) Does this look familiar?

  6. Differentiating cosine Sketch the slope of y=cos(x) Does this look familiar?

  7. Conceptest 1

  8. Conceptest 1 solution

  9. Conceptest 2

  10. Conceptest 2 solution

  11. Conceptest 3 (Hint: where is df/dx=0?)

  12. Conceptest 3 solution

  13. Conceptest 4 (Hint: calculate the slope)

  14. Conceptest 4 solution

  15. Differentiating tangent tan(x) = sin(x)/cos(x) 1. Use identity sin2x+cos2x=1 to derive tan2x+1=_____ 2. Use product or quotient rule to find d(tan(x))/dx

  16. Practice differentiating trig functions Drill on Ch.3.5 odd # problems through 41 (p.131) (skip #19) #5: y = sin(3x) = sin z where z=__________

  17. 3.6: Applications of the chain rule Finding the derivative of an inverse function (133) What is df/dx if f=x½? Trick: Write f2=x Differentiate Solve for df/dx= (Compare to result from polynomial rule.)

  18. Using chain rule to find d/dx(lnx) Recall that elnx=x. Differentiate Practice p.136 on odd problems through #15

  19. Using chain rule to find d/dx(ax) Recall that ln(ax)=x ln a. Differentiate Practice p.136 odd problems thru #35 (skip arc_ probs)

  20. Chain rule for related rates Practice p.137 #46, 48

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