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find dy/dx for sqrt of (9+ ((x9)/6)^1/5) ?
i don't know how to do this...
 one year ago
 one year ago
find dy/dx for sqrt of (9+ ((x9)/6)^1/5) ? i don't know how to do this...
 one year ago
 one year ago

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Rosh007Best ResponseYou've already chosen the best response.3
I think nesting of differentiation is a good idea.. \[\huge \frac{ d }{ dx } (\sqrt{9+(\frac{ x9 }{ 6 })^{\frac{ 1 }{ 5 }}})\] \[\huge \frac{ d }{ dx } (x^{n+1}) = (n+1)x^{n}\] then use the chain rule \[\huge \sqrt{x} = x^{\frac{ 1 }{ 2}}\] hope this will assist you
 one year ago

sha0403Best ResponseYou've already chosen the best response.0
i still did not get it.. can u teach me in detail?
 one year ago

Rosh007Best ResponseYou've already chosen the best response.3
I don't know I will be able to complete, thre is a chance of power failure here.. but let me try
 one year ago

Rosh007Best ResponseYou've already chosen the best response.3
ok... as a first we need to know chain rule of differentiation
 one year ago

Rosh007Best ResponseYou've already chosen the best response.3
as an example \[\huge \frac{ d }{ dx } (\sqrt{a+x^{n}}) = \frac{ d }{ dx } ({a+x^{n}})^\frac{ 1 }{ 2 }\]
 one year ago

Rosh007Best ResponseYou've already chosen the best response.3
a function of x... and find the derivative by function by function using the chain rule...(function by function differntiation)
 one year ago

Rosh007Best ResponseYou've already chosen the best response.3
here first function is square root (raised to 1/2) second function of x is \[\large x^{n}\] chain rule states that \[\huge \frac{ d }{ dx }(f(g(x))) = f^{'}(g(x))\times g^{'}(x)\]
 one year ago

Rosh007Best ResponseYou've already chosen the best response.3
here in this example square root is f(x) and \[\large x^{n}\] is g(x) Hope that now you can some what understand
 one year ago

sha0403Best ResponseYou've already chosen the best response.0
i think i get a little what do u say...
 one year ago

Rosh007Best ResponseYou've already chosen the best response.3
so the answer for the example becomes \[\huge (a+x^{n})^{\frac{ 1 }{ 2 }} \times (0+n \times x^{n1}) \] which is equal to \[\huge (a+x^{n})^{\frac{ 1 }{ 2 }} \times(n \times x^{n1}) \]
 one year ago

Rosh007Best ResponseYou've already chosen the best response.3
hope you under stood... so comming back to your question can you say how many functions are there in your qustion?
 one year ago

Rosh007Best ResponseYou've already chosen the best response.3
try to figure out what is the functions... and how you can apply chain rule.... and refer example when in doubt... i listd the needed formule in my first reply...(expect chain rule, which is listed in above comments)
 one year ago

Rosh007Best ResponseYou've already chosen the best response.3
yes you are right... two functions... I think powerfailure will be happening in a minute :(
 one year ago

sha0403Best ResponseYou've already chosen the best response.0
ok..then i try i get 1/2((9+(x9)/6)^1/5)^1/2 . 1/30((x9)/6)^4/5) its right or not?
 one year ago

Rosh007Best ResponseYou've already chosen the best response.3
yes .. it is right......(sorry for late reply) glad you figured out
 one year ago
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