If y = 243(4x + 5)^-2, find \(\frac{dy}{dx}\) when x = 1

addy6996

2 years ago

wrong.

Ann_e

1 year ago

We are given the function:


y = 243(4x + 5)^{-2}


We are asked to find:

{dy}/{dx}{when} x = 1

Step 1: Differentiate

Use the chain rule:

Let u = 4x + 5 , so:


y = 243u^{-2}
=>{dy}/{dx} = 243* (-2)u^{-3}*{du}/{dx}

{du}/{dx} = 4 , we get:

{dy}/{dx} = 243* (-2)*u^{-3}* 4 = -1944(4x + 5)^{-3}

Step 2: Plug in x = 1

{dy}/{dx} = -1944(4(1) + 5)^{-3} = -1944(9)^{-3}

9^3 = 729 =>{dy}/{dx} = {1944}/{729}

Now simplify:

{1944}/{729} ={72*27}/{27* 27} = {72}*{27} = {8}/{3}

So:

{dy}/{dx} = -{8}{3}

Final Answer:

A. \boxed{-\frac{8}{3}}