Is the 10 taking away 5 or was it meant to me 10.5 ?
Answer:
The inner function is
and the outer function is
.
The derivative of the function is
.
Step-by-step explanation:
A composite function can be written as
, where
and
are basic functions.
For the function
.
The inner function is the part we evaluate first. Frequently, we can identify the correct expression because it will appear within a grouping symbol one or more times in our composed function.
Here, we have
inside parentheses. So
is the inner function and the outer function is
.
The chain rule says:
![\frac{d}{dx}[f(g(x))]=f'(g(x))g'(x)](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%28g%28x%29%29%5D%3Df%27%28g%28x%29%29g%27%28x%29)
It tells us how to differentiate composite functions.
The function
is the composition,
, of
outside function: ![g(x)=3x^5](https://tex.z-dn.net/?f=g%28x%29%3D3x%5E5)
inside function: ![h(x)=4x^2 + 8](https://tex.z-dn.net/?f=h%28x%29%3D4x%5E2%20%2B%208)
The derivative of this is computed as
![\frac{d}{dx}\left(3\left(4x^2+8\right)^5\right)=3\frac{d}{dx}\left(\left(4x^2+8\right)^5\right)\\\\\mathrm{Apply\:the\:chain\:rule}:\quad \frac{df\left(u\right)}{dx}=\frac{df}{du}\cdot \frac{du}{dx}\\f=u^5,\:\:u=\left(4x^2+8\right)\\\\3\frac{d}{du}\left(u^5\right)\frac{d}{dx}\left(4x^2+8\right)\\\\3\cdot \:5\left(4x^2+8\right)^4\cdot \:8x\\\\120x\left(4x^2+8\right)^4](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%283%5Cleft%284x%5E2%2B8%5Cright%29%5E5%5Cright%29%3D3%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%28%5Cleft%284x%5E2%2B8%5Cright%29%5E5%5Cright%29%5C%5C%5C%5C%5Cmathrm%7BApply%5C%3Athe%5C%3Achain%5C%3Arule%7D%3A%5Cquad%20%5Cfrac%7Bdf%5Cleft%28u%5Cright%29%7D%7Bdx%7D%3D%5Cfrac%7Bdf%7D%7Bdu%7D%5Ccdot%20%5Cfrac%7Bdu%7D%7Bdx%7D%5C%5Cf%3Du%5E5%2C%5C%3A%5C%3Au%3D%5Cleft%284x%5E2%2B8%5Cright%29%5C%5C%5C%5C3%5Cfrac%7Bd%7D%7Bdu%7D%5Cleft%28u%5E5%5Cright%29%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%284x%5E2%2B8%5Cright%29%5C%5C%5C%5C3%5Ccdot%20%5C%3A5%5Cleft%284x%5E2%2B8%5Cright%29%5E4%5Ccdot%20%5C%3A8x%5C%5C%5C%5C120x%5Cleft%284x%5E2%2B8%5Cright%29%5E4)
The derivative of the function is
.
Answer:
The answer is, The fastest speed is 3/4 mile in 1/8 hour
Step-by-step explanation:
the answer i have = 6miles per hour and the rest of the answers are lower than that.
2 bc you can’t write it as a fraction