What is the derivative of # ln (x^8)/ x^2#?
1 Answer
Dec 17, 2015
You can do this using the product rule or the quotient rule. The product rule can be easier to simplify.
These two derivatives will be used overall:
#d/(dx)[ln(x^8)] = (8x^7)/(x^8) = 8/x#
#d/(dx)[1/x^2] = -2/x^3#
So, what we can do is:
PRODUCT RULE
#\mathbf(d/(dx)[g(x)h(x)] = g(x)(dh(x))/(dx) + h(x)(dg(x))/(dx))#
#d/(dx)[ln(x^8)*1/x^2] = ln(x^8)(-2/x^3) + 1/x^2 8/x#
#= -(2ln(x^8))/x^3 + 8/x^3#
#= color(blue)(1/x^3 [8 - 2ln(x^8)])#
