Answer:

Step-by-step explanation:

Answer:

• let f(x) be m:

• make x the subject of the function:
![{ \rm{8m = {x}^{3} + 128}} \\ \\ { \rm{ {x}^{3} = 8m - 128 }} \\ \\ { \rm{ {x}^{3} = 8(m - 16) }} \\ \\ { \rm{x = \sqrt[3]{8} \times \sqrt[3]{(m - 16)} }} \\ \\ { \rm{x = 2 \sqrt[3]{(m - 16)} }}](https://tex.z-dn.net/?f=%7B%20%5Crm%7B8m%20%3D%20%20%7Bx%7D%5E%7B3%7D%20%20%2B%20128%7D%7D%20%5C%5C%20%20%5C%5C%20%7B%20%5Crm%7B%20%7Bx%7D%5E%7B3%7D%20%3D%208m%20-%20128%20%7D%7D%20%5C%5C%20%20%5C%5C%20%7B%20%5Crm%7B%20%7Bx%7D%5E%7B3%7D%20%3D%208%28m%20-%2016%29%20%7D%7D%20%5C%5C%20%20%5C%5C%20%7B%20%5Crm%7Bx%20%3D%20%20%5Csqrt%5B3%5D%7B8%7D%20%20%5Ctimes%20%20%5Csqrt%5B3%5D%7B%28m%20-%2016%29%7D%20%7D%7D%20%5C%5C%20%20%5C%5C%20%7B%20%5Crm%7Bx%20%3D%202%20%5Csqrt%5B3%5D%7B%28m%20-%2016%29%7D%20%7D%7D)
• therefore:

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You can actually use either the product rule or the chain rule for this one. Observe:
• Method I:y = cos² xy = cos x · cos xDifferentiate it by applying the product rule:

The derivative of
cos x is
– sin x. So you have


—————
• Method II:You can also treat
y as a composite function:

and then, differentiate
y by applying the chain rule:

For that first derivative with respect to
u, just use the power rule, then you have

and then you get the same answer:

I hope this helps. =)
Tags: <em>derivative chain rule product rule composite function trigonometric trig squared cosine cos differential integral calculus</em>
Answer:
1) 
2) 
3) 
Step-by-step explanation:
To write logs of the form
in their exponential form, you take the base b and put it to the power of x and then set that equal to a:
.
1. Here, b = 5, a = 25, and x = 2, so: 
2. In this problem, b = 5, x = 2, and a = x, so: 
3. Finally, here, b = b, a = 64, and x = 3, so: 
Hope this helps!
Answer:
13. Answer: 0
17. Answer: 3
19. Answer: 2
Step-by-step explanation:
13. f(g(3))
First find g(3) on the right graph.
We see that at x = 3, g(x) = 4
So g(3) = 4
Next find f(g(3)). Since g(3) = 4, that means we have to find f(4) and the from the left graph we see that f(4) = 0 answer
17.f(f(5))
f(5) = 1
f(f(5)) = f(1) = 3 answer
19. g(g(2))
g(2) = 0
g(g(2)) = g(0) = 2 answer