Question

Use logarithmic differentiation to calculate y prime....Please show work

y= ((x-1)^5) * (x+2)^(1/4))/((x^2+7)^(1/2))

Answer 1

is it like this?
\[y=\frac{(x-1)^5(x+2)^\frac{1}{4}}{(x^2+7)^\frac{1}{2}}\]

Answer 2

yes

Answer 3

first you want to take ln of both sides:
\[\ln y = \ln \left(\frac{(x−1)^5(x+2)^\frac{1}{4}}{(x^2+7)^\frac{1}{2}}\right)\]

then using properties of ln, such as:\[\ln (a\cdot b)=\ln a + \ln b\]and\[\ln \left(\frac{a}{b}\right)=\ln a - \ln b\]and\[\ln x^a = a \ln x\]re write the right side as sums/differences/products to make it easier to take the derivative of.