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sha0403
 3 years ago
find dy/dx for sqrt of (9+ ((x9)/6)^1/5) ?
i don't know how to do this...
sha0403
 3 years ago
find dy/dx for sqrt of (9+ ((x9)/6)^1/5) ? i don't know how to do this...

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Rosh007
 3 years ago
Best ResponseYou've already chosen the best response.3I 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

sha0403
 3 years ago
Best ResponseYou've already chosen the best response.0i still did not get it.. can u teach me in detail?

Rosh007
 3 years ago
Best ResponseYou've already chosen the best response.3I don't know I will be able to complete, thre is a chance of power failure here.. but let me try

Rosh007
 3 years ago
Best ResponseYou've already chosen the best response.3ok... as a first we need to know chain rule of differentiation

Rosh007
 3 years ago
Best ResponseYou've already chosen the best response.3as an example \[\huge \frac{ d }{ dx } (\sqrt{a+x^{n}}) = \frac{ d }{ dx } ({a+x^{n}})^\frac{ 1 }{ 2 }\]

Rosh007
 3 years ago
Best ResponseYou've already chosen the best response.3a function of x... and find the derivative by function by function using the chain rule...(function by function differntiation)

Rosh007
 3 years ago
Best ResponseYou've already chosen the best response.3here first function is square root (raised to 1/2) second function of x is \[\large x^{n}\] chain rule states that \[\huge \frac{ d }{ dx }(f(g(x))) = f^{'}(g(x))\times g^{'}(x)\]

Rosh007
 3 years ago
Best ResponseYou've already chosen the best response.3here in this example square root is f(x) and \[\large x^{n}\] is g(x) Hope that now you can some what understand

sha0403
 3 years ago
Best ResponseYou've already chosen the best response.0i think i get a little what do u say...

Rosh007
 3 years ago
Best ResponseYou've already chosen the best response.3so the answer for the example becomes \[\huge (a+x^{n})^{\frac{ 1 }{ 2 }} \times (0+n \times x^{n1}) \] which is equal to \[\huge (a+x^{n})^{\frac{ 1 }{ 2 }} \times(n \times x^{n1}) \]

Rosh007
 3 years ago
Best ResponseYou've already chosen the best response.3hope you under stood... so comming back to your question can you say how many functions are there in your qustion?

Rosh007
 3 years ago
Best ResponseYou've already chosen the best response.3try 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)

Rosh007
 3 years ago
Best ResponseYou've already chosen the best response.3yes you are right... two functions... I think powerfailure will be happening in a minute :(

sha0403
 3 years ago
Best ResponseYou've already chosen the best response.0ok..then i try i get 1/2((9+(x9)/6)^1/5)^1/2 . 1/30((x9)/6)^4/5) its right or not?

Rosh007
 3 years ago
Best ResponseYou've already chosen the best response.3yes .. it is right......(sorry for late reply) glad you figured out
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