find second derivatice

label Calculus
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x^3/5(10-x) ^2/5

Jul 31st, 2015

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x^3/5(10-x) ^2/5


please give me the first derivative ?

then i will solve that for you

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Jul 31st, 2015

x^3/5(10-x) ^2/5

[x^3(10-x) ^2 ]^ 1/5

[x^3(x^2 +100 - 2x) ]^ 1/5

[x^5 +100x^3 - 2x^4) ]^ 1/5

first derivative

d/dx [x^5 +100x^3 - 2x^4) ]^ 1/5

1/5 [x^5 +100x^3 - 2x^4) ]^ (1/5-1) d/dx[x^5 +100x^3 - 2x^4) ]

1/5 [x^5 +100x^3 - 2x^4) ]^ (-4/5) [5x^4 +300x^2 - 8x^3) ]

Now second derivative

d/dx 1/5 [x^5 +100x^3 - 2x^4) ]^ (-4/5) [5x^4 +300x^2 - 8x^3) ]

using product rule of derivative

1/5 d/dx [x^5 +100x^3 - 2x^4) ]^ (-4/5) [5x^4 +300x^2 - 8x^3) ]+ 1/5 [x^5 +100x^3 - 2x^4) ]^ (-4/5) d/dx [5x^4 +300x^2 - 8x^3) ]

-4/25 [x^5 +100x^3 - 2x^4) ]^ (-4/5 -1) [5x^4 +300x^2 - 8x^3) ]^2 + 1/5 [x^5 +100x^3 - 2x^4) ]^ (-4/5) [20x^3 +600x - 24x^2) ]

-4/25 [x^5 +100x^3 - 2x^4) ]^(-9/5) [5x^4 +300x^2 - 8x^3) ]^2 + 1/5 [x^5 +100x^3 - 2x^4)]^(-4/5) [20x^3 +600x - 24x^2) ] answer


Jul 31st, 2015

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