Question

Using Logarithmic Differentiation, find the derivative of y=((2x+1)^5)*(((x^4)-3)^6)

Answer 1

\[y=(2x+1)^5(x^4-3)^6\]

Answer 2

\[\ln y=5\ln(2x+1)+6\ln(x^4-3)\]

Answer 3

\[\frac {y'}{y}=5*\frac{2}{2x+1}+6*\frac{4x^3}{x^4-3}\]

Answer 4

\[y'=y \left[5*\frac{2}{2x+1}+6*\frac{4x^3}{x^4-3} \right]\]

Answer 5

\[y'=(2x+1)^5(x^4-3)^6\left[\frac{10}{2x+1}+\frac{24x^3}{x^4-3} \right]\]

Answer 6

Thanks! Funny thing was I figured it out before you finished it. But thanks anyways! :)

Answer 7

I was just trying to make it clear..