Question

All parts of this problem refer to the function below. $y = (9 + 2x)^{4/x}$ a) Use logarithmic differentiation to find $frac{dy}{dx}$ $frac{dy}{dx} = left(frac{-4ln(9 + 2x)}{x^2} + frac{8}{9x + 2x^2} ight)(9 + 2x)^{frac{4}{x}}$ b) Find the slope of the tangent line at $x = 1$. Slope = -129782.34 c) Find the equation of the tangent line at $x = 1$. Tangent line: $y = -129782.34x - 144423.34$

          All parts of this problem refer to the function below.
$y = (9 + 2x)^{4/x}$
a) Use logarithmic differentiation to find $frac{dy}{dx}$
$frac{dy}{dx} = left(frac{-4ln(9 + 2x)}{x^2} + frac{8}{9x + 2x^2}
ight)(9 + 2x)^{frac{4}{x}}$
b) Find the slope of the tangent line at $x = 1$.
Slope = -129782.34
c) Find the equation of the tangent line at $x = 1$.
Tangent line: $y = -129782.34x - 144423.34$

$All parts of this problem refer to the function below. y = (9 + 2x)^4/x a) Use logarithmic differentiation to find fracdydx fracdydx = left(frac-4ln(9 + 2x)x^2 + frac89x + 2x^2 ight)(9 + 2x)^frac4x b) Find the slope of the tangent line at x = 1. Slope = -129782.34 c) Find the equation of the tangent line at x = 1. Tangent line: y = -129782.34x - 144423.34$

Added by Brian M.

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