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Here is a set of practice problems to accompany the Product and Quotient Rule section of the Derivatives chapter of the notes for Paul Dawkins Calculus I course at Lamar University.
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These Calculus Worksheets will produce problems that involve using the quotient rule to differentiate functions. The student will be given rational functions and will be asked to differentiate them using the quotient rule.
The Quotient Rule. In this worksheet, we will derive a formula for the derivative of a function of the form . From. here on out, let f(x) and g(x) be di erentiable functions. 1. Let Q(x) = . By multiplying both sides of this equation by g(x) and then applying the g(x) product rule, nd a formula for f0(x) in terms of Q(x), Q0(x), g(x), and g0(x).
The Quotient Rule. A special rule, the quotient rule, exists for differentiating quotients of two functions. This unit illustrates this rule. In order to master the techniques explained here it is vital that you undertake plenty of practice exercises so that they become second nature.
Quotient Rule worksheet MATH 1500 Find the derivative of each of the following functions by using the quotient rule. 1. 11 p x (5x2 +12x+1) 2. log12 (x) p x 3. ex (x3 +15) 4. 12 p x cot(x) 5. ln(x) (¡22x+8) 6. tan(x) p x 7. tan(x) (x3 +15) 8. cos(x) cot(x) 9. x31 cos(x) 10. (¡sin(x)) (5x2 +12x+1) 11. ex (¡cos(x)) 12. x100 cot(x) 13. ln(x) 14 ...
The Quotient Rule. dx. f(x) g(x) f0(x)g(x) f(x)g0(x) = (g(x))2. If we need to take the derivative of two functions being divided, we cannot simply divide the derivative of the numerator by the derivative of the denominator; dx. f(x) g(x) f0(x) 6= : g0(x) Example 1: Compute the derivative of the following function. sin(x) + x. y = 2x + 1.