SOLUTION: All parts of this problem refer to the function below.
y=(6+3x)5/x
a) Use logarithmic differentiation to find dy/dx
dydx=
b) Find the slope of the tangent line at x=1.
Slope
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Question 1187766: All parts of this problem refer to the function below.
y=(6+3x)5/x
a) Use logarithmic differentiation to find dy/dx
dydx=
b) Find the slope of the tangent line at x=1.
Slope =
c) Find the equation of the tangent line at x=1.
Tangent line: y=
Answer by Solver92311(821) (Show Source): You can put this solution on YOUR website!
Sunday, April 2, 2017
7:06 PM
^{5/x})
\ =\ \ln\(\(6\,+\,3x\)^{5/x}\))
\ =\ \frac{5}{x}\,\ln\(6\,+\,3x\))
\])
\(\ln\(6\,+\,3x\)\)\ +\ \(\frac{5}{x}\)\(\frac{d}{dx}\,\ln\(6\,+\,3x\)\))
\(\ln\(6\,+\,3x\)\)\ +\ \(\frac{5}{x}\)\(\frac{1}{6\,+\,3x}\)\,\frac{d}{dx}(6\,+\,3x))
\(\ln\(6\,+\,3x\)\)\ +\ \(\frac{15}{x}\)\(\frac{1}{6\,+\,3x}\))
^{5/x}\[\(-\frac{5}{x^2}\)\(\ln\(6\,+ \,3x\)\)\ +\ \(\frac{15}{x}\)\(\frac{1}{6\,+\,3x}\)\])
For part b, evaluate )
For part c,
\ =\ y'(1)(x\,-\,1))
You can do your own arithmetic.
John
My calculator said it, I believe it, that settles it
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