Question

estimate the derivative of f(x)=x^x at x=2

Answer 1

Estimate using which method?

Answer 2

if it really means "estimate" whip out your calculator and try
\[\frac{(2.001)^{2.001}-2^2}{.001}\]

Answer 3

if you want to find the "actual value" you will either have to use logarithmic differentiation or else write
\[f(x)=x^x=e^{x\ln(x)}\] and take the derivative using the chain rule and the product rule.

Answer 4

for the example i did above i got 6.779 rounded. if you want a better estimate pick a decimal even closer to 2. for example try
\[\frac{(2.000001)^{2.000001}-4}{.000001}\]

Answer 5

thanks so much

Answer 6

yw