How do you find the derivative of #f(x)=1/(2x+5)^5#?

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Answer 1 · 2016-11-30T14:02:04

#dy/dx= -10/(2x+ 5)^6#

We convert this function to #f(x) = (2x + 5)^-5#. We make #y = u^-5# and #u = 2x + 5#.

Hence, by the power rule, #dy/(du) = -5u^-6# and #(du)/dx = 2#

The chain rule states that #dy/dx= dy/(du) xx (du)/dx#.

#dy/dx= -5u^4 xx 2#

#dy/dx = -10(2x + 5)^-6#

#dy/dx= -10/(2x+ 5)^6#

Hopefully this helps!