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## sha0403 Group Title find dy/dx for sqrt of (9+ ((x-9)/6)^1/5) ? i don't know how to do this... one year ago one year ago

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1. Rosh007 Group Title

I think nesting of differentiation is a good idea.. $\huge \frac{ d }{ dx } (\sqrt{9+(\frac{ x-9 }{ 6 })^{\frac{ 1 }{ 5 }}})$ $\huge \frac{ d }{ dx } (x^{n+1}) = (n+1)x^{n}$ then use the chain rule $\huge \sqrt{x} = x^{\frac{ 1 }{ 2}}$ hope this will assist you

2. sha0403 Group Title

i still did not get it.. can u teach me in detail?

3. Rosh007 Group Title

I don't know I will be able to complete, thre is a chance of power failure here.. but let me try

4. Rosh007 Group Title

ok... as a first we need to know chain rule of differentiation

5. Rosh007 Group Title

as an example $\huge \frac{ d }{ dx } (\sqrt{a+x^{n}}) = \frac{ d }{ dx } ({a+x^{n}})^\frac{ 1 }{ 2 }$

6. Rosh007 Group Title

a function of x... and find the derivative by function by function using the chain rule...(function by function differntiation)

7. Rosh007 Group Title

here first function is square root (raised to 1/2) second function of x is $\large x^{n}$ chain rule states that $\huge \frac{ d }{ dx }(f(g(x))) = f^{'}(g(x))\times g^{'}(x)$

8. Rosh007 Group Title

here in this example square root is f(x) and $\large x^{n}$ is g(x) Hope that now you can some what understand

9. sha0403 Group Title

i think i get a little what do u say...

10. Rosh007 Group Title

so the answer for the example becomes $\huge (a+x^{n})^{\frac{ -1 }{ 2 }} \times (0+n \times x^{n-1})$ which is equal to $\huge (a+x^{n})^{\frac{ -1 }{ 2 }} \times(n \times x^{n-1})$

11. Rosh007 Group Title

hope you under stood... so comming back to your question can you say how many functions are there in your qustion?

12. sha0403 Group Title

about 2 function?

13. Rosh007 Group Title

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)

14. Rosh007 Group Title

yes you are right... two functions... I think powerfailure will be happening in a minute :(

15. sha0403 Group Title

ok..then i try i get 1/2((9+(x-9)/6)^1/5)^-1/2 . 1/30((x-9)/6)^-4/5) its right or not?

16. Rosh007 Group Title

yes .. it is right......(sorry for late reply) glad you figured out