Let k(x) = f(x)g(x). Use the graphs above to find the following derivatives.k '(1) = k '(3) =

Use the given graph to estimate the value of each derivative. (Round all answers to one decimal place.)(a) f ' (-3) (b) f ' (-2) (c) f ' (-1) (d) f ' (0) (e) f ' (1) (f) f ' (2) (g) f ' (3)

Use the given graph to estimate the value of each derivative.(a)f '(0) (b)f '(1) (c)f '(2) (d)f '(3) (e)f '(4) (f)f '(5)

If f and g are the functions whose graphs are shown, let u(x) = f(g(x)), v(x) = g(f(x)), and w(x) = g(g(x)). Find each derivative, if it exists. If it does not exist, explain why. (If an answer does not exist, enter DNE.)(a)    u'(1) = It does exist.u'(1) does not exist because f '(1) does not exist.    u'(1) does not exist because g'(1) does not exist.u'(1) does not exist because f '(3) does not exist.u'(1) does not exist because g'(2) does not exist.(b)    v'(1) = It does exist.v'(1) does not exist because f '(1) does not exist.    v'(1) does not exist because g'(1) does not exist.v'(1) does not exist because f '(3) does not exist.v'(1) does not exist because g'(2) does not exist.(c)    w'(1) = Your answer cannot be understood or graded. More InformationIt does exist.w'(1) does not exist because f '(1) does not exist.    w'(1) does not exist because g'(1) does not exist.w'(1) does not exist because f '(3) does not exist.w'(1) does not exist because g'(2) does not exist.

f(x)h(−2)h′(−2)g(−2)g′(−2)k(−2)k′(−2)=======x2h(x)+4k(x)h(x)g(x)+x44k(x)−6−9−52−6−8𝑓⁡(𝑥)=◂+▸ℎ⁡(−2)=−6ℎ′⁡(−2)=−9𝑔⁡(−2)=−5𝑔′⁡(−2)=2𝑘⁡(−2)=−6𝑘′⁡(−2)=−8 Taskf′(−2)=◂=▸AnswerCheckQuestion 5

Suppose that f(5) = 1, f '(5) = 8, g(5) = −4, and g'(5) = 2. Find the following values.(a)    (fg)'(5) (b)    (f/g)'(5) (c)    (g/f)'(5)