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Differentiate with respect to x: y=4x-5ax^(-5)

Guest Oct 1, 2017
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 #1
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Possible derivation:
d/dx(-(5 a)/x^5 + 4 x)

Differentiate the sum term by term and factor out constants:
 = -5 a (d/dx(1/x^5)) + 4 (d/dx(x))

Use the power rule, d/dx(x^n) = n x^(n - 1), where n = -5: d/dx(1/x^5) = d/dx(x^(-5)) = -5 x^(-6):
 = 4 (d/dx(x)) - (-5)/x^6 5 a

Simplify the expression:
 = (25 a)/x^6 + 4 (d/dx(x))

The derivative of x is 1:
 = (25 a)/x^6 + 1 4

Simplify the expression:
= 4 + (25 a)/x^6

Guest Oct 1, 2017
 #2
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 y = 4x - (5a)x^(-5)  

 

dy / dx  =  4 + (25a)x^(-6)

 

 

cool cool cool

CPhill  Oct 1, 2017

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