6 A Find the derivative of each of the following functions using derivative rules. Remember to...
1. Find and simplify the derivative of each of the following functions: In(2 1) 2x 1) tan 1In(tan) (a) (x)In (b) f(x) = (412-1)3 In(4z?-1) (g) f(r)-n (n) f(x) = ln(sec 3r-tan 3r) 1 +x ln a
2. (each 1 mark) Find the derivative of the following functions: 9x + 7 (a) y = 92 - 1 (b)r = (02 9016 /09 - 9 ( 9 ) (c) y=rºcot x + 9x2 cos x – 14x sin x 9t sint (d) s = cost + +9 (e) h(x) = cº sin (vą) + 240 sec (1) ) 10 (f) f(0) = (_sin 98 (1+cos 90 ) (g) g(x) = (1 + csc(+10) + In (922 – 8)...
10. Use the limit definition of the derivative to calculate the derivatives of the following functions. a. f(x) = 2x2 – 3x + 4 b. g(x) = = x2 +1 1 x2 +1 c. h(x) = 3x - 2 a. 11. Find the derivative with respect to x. x² - 4x f(x)= b. y = sec v c. 5x2 – 2xy + 7y2 = 0 1+cos x 1-cosx cos(Inu) e. S(x) = du 1+1 + + f. y =sin(x+y) g....
21. Find the derivative of each of the following functions by applying the product rule a. f(x) = (x2 + 1][2x2 + 3x + 4) b. f(x) = x2 cos x c. f(x) = e* sin x 22. Find Find the derivative of each of the following functions by applying the quotient rule a. f(x) = 22+1 f(x) = (2x + 1] / [x - 3] b. f(x) = x+2x+1 3x + 1 c. f(x) = sing 23. Find the...
MTH 261-A Test unit ! | Ench part of each problem Counds 7pts. 1. Find the domain of the function I f(x) = x - 4 2. Compute each limit. 3. Find the derivative dy for each function, Simplify results. all y = 5x + 4x² b. y = 6 x - 3 4. Find the second derivative of f(x). Simplify results. f(x) = (x²+2)5 so Write the equation of the line tan to the graph of y=x²-2x+7 I at...
11. (5 points each) Find the derivative of each function. DO NOT simplify your answers. cos(x) a) f(x) = 1-tan(x) b) f(x) – tan-" (4x²) dy 12. Consider the equation x² + xy + y² = 1. Find an expression for by implicit differentiation. dx
For the following exercises, find (fºg)(x) and ( gn) for each pair of functions. 34. f(x) = 4 – x, g(x) = - 4x 35. f(x) = 3x + 2, g(x) = 5 - 6x 36. f(x) = x2 + 2x, g(x) = 5x + 1 37. f(x) = Vx+2, g(x) = 38. f(x)= x +3 1, g(x) = V1 - x
Below are eight functions. Find the first derivative of each. Space is provided. Use good dark ink if you are returning this by a scanned version. All of the derivatives can be found by using combinations of the constant rule, power function rule and sum-difference rule. Do not use the product rule. It is not needed. The degree of difficulty (more or less) increases from (a-h). Be sure to show intermediate work. Check the scoring rubric to see how the points are awarded. For example, the first...
Q1) Evaluate the partial derivative with respect to x of each of the following functions d) f(x, y)2y In(x) e) f(x, y) = 2x-2-tu
1. Find the slope for each of the functions below: (a) y = f(x) = 52 (b) y = f(x) = 1 3 x 3 + x 2 + 4x − 10 (c) y = f(x) = 1 3 x 3 + x 2 + 4x + 400 (d) y = f(x) = x 1 2 (e) = f(x) = 4x 1 2 + x 2 − .1x 3 − 5 (f) = f(x) = 4x + 6 (g) y...