You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an alternative browser.
You should upgrade or use an alternative browser.
logarithmic differentiation problem
- Thread starter eiei0
- Start date
\(\displaystyle y=(x-2)^{x+1}\)
Take ln of both sides:
\(\displaystyle ln(y)=(x+1)ln(x-2)\)
Differentiate both sides:
\(\displaystyle \frac{y'}{y}=ln(x-2)+\frac{x+1}{x-2}\)
Solve for y':
\(\displaystyle y'=y\left(ln(x-2)+\frac{x+1}{x-2}\right)\)
Remember that \(\displaystyle y=(x-2)^{x+1}\) and sub it in:
\(\displaystyle y'=(x-2)^{x+1}\cdot\left(ln(x-2)+\frac{x+1}{x-2}\right)\)
See now how to do them?.
Take ln of both sides:
\(\displaystyle ln(y)=(x+1)ln(x-2)\)
Differentiate both sides:
\(\displaystyle \frac{y'}{y}=ln(x-2)+\frac{x+1}{x-2}\)
Solve for y':
\(\displaystyle y'=y\left(ln(x-2)+\frac{x+1}{x-2}\right)\)
Remember that \(\displaystyle y=(x-2)^{x+1}\) and sub it in:
\(\displaystyle y'=(x-2)^{x+1}\cdot\left(ln(x-2)+\frac{x+1}{x-2}\right)\)
See now how to do them?.