Question

for the curve xy=4, dy/dx at (2,2)=?​

Answer 1

Step-by-step explanation:

Hope it helps uuh.

....

Answer 2

$\displaystyle \sf{ \frac{dy}{dx} \: at \: (2,2) }= - 1$

Given :

The equation of the curve xy = 4

To find :

$\displaystyle \sf{ \frac{dy}{dx} \: at \: (2,2) }$

Solution :

Step 1 of 2 :

Write down the given equation

Here the given equation of the curve is xy = 4

Step 2 of 2 :

Find dy/dx

xy = 4

$\displaystyle \sf{ \implies y = \frac{4}{x} }$

Differentiating both sides with respect to x we get

$\displaystyle \sf{ \frac{dy}{dx} = \frac{d}{dx} \bigg( \frac{4}{x} \bigg) }$

$\displaystyle \sf{ \implies \frac{dy}{dx} = 4\frac{d}{dx} \bigg( \frac{1}{x} \bigg)}$

$\displaystyle \sf{ \implies \frac{dy}{dx} = - \frac{4}{ {x}^{2} } }$

$\displaystyle \sf{ \therefore \: \frac{dy}{dx} \: at \: (2,2) }$

$\displaystyle \sf{ = \frac{dy}{dx} \bigg|_{(2,2) }}$

$\displaystyle \sf{ = - \frac{4}{ {2}^{2} } }$

$\displaystyle \sf{ = - \frac{4}{ 4 } }$

$\displaystyle \sf{ = - 1 }$

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ let 5f(x)+ 3f(1/x)=x+2 and y= xf(x) . then x=1 point dy/dx=?

https://brainly.in/question/19870192

2. Let f(1) = 3,f' (1)=- 1/3,g (1)=-4 and g' (1) =-8/3

The derivative of √[[f(x)]^2+ [g (x)]^2] W. r. to. x. is

https://brainly.in/question/18312318