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anonymous
 one year ago
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
anonymous
 one year ago
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

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Sorry, I made a typo. \[f(x) = 8\sin^3(x^{1/2})\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0actually 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

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0sorry, thanks for all your help, im just on a time crunch.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0You're not taking a test are you?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no, I just have to be somewhere soon

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0And this homework is due tomorrow

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So i assume : \[(g~\circ ~ f)'(x) \qquad \implies \qquad \frac{d}{dx}(g(f(x)) = g'(f(x)) \cdot f'(x)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ack, I've got to head off for a little while, I will be back very soon.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@DanJS @jim_thompson5910 mind taking over? Thanks!

DanJS
 one year ago
Best ResponseYou've already chosen the best response.0i am late, are you still working on these things?

DanJS
 one year ago
Best ResponseYou've already chosen the best response.0yes, 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
 one year ago
Best ResponseYou've already chosen the best response.0f(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
 one year ago
Best ResponseYou've already chosen the best response.0To find f'(x) you use the chain rule... \[\frac{ d }{ dx }f(x) = \frac{ d }{ du }*\frac{ du }{ dx } f(x)\]

DanJS
 one year ago
Best ResponseYou've already chosen the best response.0If 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
 one year ago
Best ResponseYou've already chosen the best response.0similar 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
 one year ago
Best ResponseYou've already chosen the best response.0simplifies to D i think ... check it out,

DanJS
 one year ago
Best ResponseYou've already chosen the best response.0keep leaving the inner functions alone, and work outside to inside, power rule  derivative of sin()  derivative of root x

DanJS
 one year ago
Best ResponseYou've already chosen the best response.0\[[f(g(h(x)))] ' = f'(g(h(x))) *g'(h(x)) * h'(x)\]

DanJS
 one year ago
Best ResponseYou've already chosen the best response.0you can have as many nested functions as you want, same idea
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