Answer:
(g ο h)(x) = -50x³ + 65x² - 15x + 15
(h ο g)(x) = -1250x³ + 325x² - 15x + 3 ⇒ 3rd answer
Step-by-step explanation:
* Lets explain the composite function
- A composite function is a function that depends on another function
- A composite function is created when one function is substituted into
another function
- Example:
# (f ο g)(x) is the composite function that is formed when g(x) is
substituted for x in f(x).
* Now lets solve the problem
∵ g(x) = 5x
∵ h(x) = -10x³ + 13x² - 3x + 3
- To find (g ο h)(x) replace x in g by h(x)
∴ Replace x by -10x³ + 13x² - 3x + 3
∴ (g ο h)(x) = 5(-10x³ + 13x² - 3x + 3)
∴ (g ο h)(x) = -50x³ + 65x² - 15x + 15
- To find (h ο g)(x) replace each x in -10x³ + 13x² - 3x + 3 by g(x)
∴ Replace each x in -10x³ + 13x² - 3x + 3 by 5x
∴ (h ο g)(x) = -10(5x)³ + 13(5x)² - 3(5x) + 3)
∴ (h ο g)(x) = -10(125x³) + 13(25x²) - 15x + 3
∴ (h ο g)(x) = -1250x³ + 325x² - 15x + 3
* (g ο h)(x) = -50x³ + 65x² - 15x + 15
(h ο g)(x) = -1250x³ + 325x² - 15x + 3
, then you can find partial derivatives: 
.
) these derivatives have values:
-- the slopes at x and y- directions, respectively.