Question

Use logarithmic differentiation to find the derivative of y = x √ x.

Answer 1

\[
y = x^1\cdot x^{1/2} = x^{3/2}
\]

Answer 2

the x is being raised to sqrt of X

Answer 3

\[
\ln(y) = \ln(x^{3/2})
\]

Answer 4

This is a good start.

Answer 5

\[
x= x^1, \sqrt{x} = x^{1/2}, x\sqrt{x} = x^{1+1/2} = x^{3/2}
\]

Answer 6

sorry the x is being raised to the power of sqrtX

Answer 7

\[X^\sqrt{X}\]

Answer 8

Okay then \[
\ln(x^{\sqrt{x}}) = \sqrt{x}\ln(x)
\]