clara1223
  • clara1223
Calculate the derivative of the given function f(x)=8sin^3(√x) a) f′(x)=24sin^2(√x)cos(√x) b) f′(x)=48sin^2(√x)cos(√x)/x√x c) f′(x)=24cos(√x) d) f′(x)=12sin^2(√x)cos(√x)/√x e) f′(x)=12cos(√x)/√x
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
clara1223
  • clara1223
yes, one second
Jhannybean
  • Jhannybean
Sorry, I made a typo. \[f(x) = 8\sin^3(x^{1/2})\]
clara1223
  • clara1223
actually could you help me with this really quickly? its more pressing: Evaluate (g∘f)′(6), given that f(4)=4, f(5)=6, f(6)=6, g(4)=5, g(5)=5, g(6)=4, f′(4)=6, f′(5)=5, f′(6)=4, g′(4)=5, g′(5)=5, g′(6)=4 a) 16 b) 19 c) 18 d) 17 e) 15

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

clara1223
  • clara1223
sorry, thanks for all your help, im just on a time crunch.
Jhannybean
  • Jhannybean
You're not taking a test are you?
clara1223
  • clara1223
no, I just have to be somewhere soon
Jhannybean
  • Jhannybean
Oh, alright.
clara1223
  • clara1223
And this homework is due tomorrow
Jhannybean
  • Jhannybean
So i assume : \[(g~\circ ~ f)'(x) \qquad \implies \qquad \frac{d}{dx}(g(f(x)) = g'(f(x)) \cdot f'(x)\]
Jhannybean
  • Jhannybean
where \(x=6\)
Jhannybean
  • Jhannybean
Ack, I've got to head off for a little while, I will be back very soon.
Jhannybean
  • Jhannybean
@DanJS @jim_thompson5910 mind taking over? Thanks!
DanJS
  • DanJS
i am late, are you still working on these things?
DanJS
  • DanJS
yes, that one would be just the chain rule, and they list the values you may need for the functions and their derivatives \[\qquad \frac{d}{dx}(g(f(6)) = g'(f(6)) \cdot f'(6) \]
DanJS
  • DanJS
f(6) = 6 f '(6) = 4 g'(6)=4 so \[\qquad \frac{d}{dx}(g(f(x)) = g'(f(x)) \cdot f'(x) = g'(6)*f'(6) = 4*4\]
DanJS
  • DanJS
To find f'(x) you use the chain rule... \[\frac{ d }{ dx }f(x) = \frac{ d }{ du }*\frac{ du }{ dx } f(x)\]
DanJS
  • DanJS
If you have a function inside a function , like f(g(x)) f(x) = sin(x^3) I usually think something like; " f ' (x) is equal to derivative of sin(inside function left alone) times the derivative of the inside function" f ' (x) = cos(x^3) * 2x^2 thats it, goodluck
DanJS
  • DanJS
similar with the given function f(x) = 8*sin(x^(1/2))^3 start with outside and leave inside function same, except here you have to use the rule two times, u^3, sin(u) and x^(1/2) start from outside power function \[f ' (x) = 3*8*[\sin(x^{1/2})]^2~*~\cos(x^{1/2})*\frac{ 1 }{ 2 }*x^{-1/2}\]
DanJS
  • DanJS
simplifies to D i think ... check it out,
DanJS
  • DanJS
keep leaving the inner functions alone, and work outside to inside, power rule - derivative of sin() - derivative of root x
DanJS
  • DanJS
\[[f(g(h(x)))] ' = f'(g(h(x))) *g'(h(x)) * h'(x)\]
DanJS
  • DanJS
you can have as many nested functions as you want, same idea

Looking for something else?

Not the answer you are looking for? Search for more explanations.