Question

(a) (8A: Parts 1, 2, and 3) Show clearly how you found the derivatives for the following functions. Do not just state the derivative function - but also indicate which derivative rules you are using. i. l(c) = (1)/(4c^(2)) iv. f(x) = (2x^(2) + 1)(x^(2) - x) ii. d(z) = (z + 1)/(sqrt{z}) v. h(x) = x(e^(x) + 3) iii. m(x) = (1)/(2)(x - 2)^(3) + 2e^(x) (b) (8B: Part 3) Find an equation for the line tangent to the function k(x) = x^(2)e^(x) at the point where x = 0.5. Graph k(x) and your equation for this line in Desmos to show that they are tangent at x = 0.5. (c) (8B: Part 4) Show - with an example - that this is NOT a true statement for the derivative of a product of functions: (d/dx)(f(x)g(x)) ≠ (d/dx)(f(x))(d/dx)(g(x)) i.e., (fg)' ≠ f'g'

          (a) (8A: Parts 1, 2, and 3) Show clearly how you found the derivatives for the following functions. Do not just state the derivative function - but also indicate which derivative rules you are using.
i. l(c) = (1)/(4c^(2))
iv. f(x) = (2x^(2) + 1)(x^(2) - x)
ii. d(z) = (z + 1)/(sqrt{z})
v. h(x) = x(e^(x) + 3)
iii. m(x) = (1)/(2)(x - 2)^(3) + 2e^(x)

(b) (8B: Part 3) Find an equation for the line tangent to the function k(x) = x^(2)e^(x) at the point where x = 0.5. Graph k(x) and your equation for this line in Desmos to show that they are tangent at x = 0.5.

(c) (8B: Part 4) Show - with an example - that this is NOT a true statement for the derivative of a product of functions:
(d/dx)(f(x)g(x)) ≠ (d/dx)(f(x))(d/dx)(g(x)) i.e., (fg)' ≠ f'g'

a 8a parts 1 2 and 3 show clearly how you found the derivatives for the following functions do not just state the derivative function but also indicate which derivative rules you are using i 71406

Added by Susan W.

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