What is the derivative of #y = ((x^2 + 5) / (x^2 - 5))^5#?

1 Answer
Noah G
Jan 12, 2018

#dy/dx= (-100x(x^2 + 5)^4)/(x^2 - 5)^6#

Explanation:

Use the chain rule.

Let #y = u^5# and #u = (x^2 + 5)/(x^2 -5)#.

#dy/dx= 5u^4 * (2x(x^2 - 5) - (2x(x^2 + 5)))/(x^2 - 5)^2#

#dy/dx = 5u^4 * (2x^3 - 10x - 2x^3 - 10x)/(x^2 -5)^2#

#dy/dx = 5u^4 * (-20x)/(x^2 -5)^2#

#dy/dx= (-100x((x^2 + 5)/(x^2 -5))^4)/(x^2 -5)^2#

#dy/dx= (-100x(x^2 + 5)^4)/(x^2 - 5)^6#

Hopefully this helps!

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