Question

Calculus y=5-(x-1)^2​

Answer 1

Answer:

$\large -2x+2$

Step-by-step explanation:

Given :

$\large y=5-(x-1)^2$

We know derivative of constant term is 0.

And here we will use power formula of differentiation.

$\large x^n=n.x^{n-1}$

So  d / d x

$\large \dfrac{d}{dx} =5-(x-1)^2\\\\\\\large \dfrac{d}{dx}(5)-\dfrac{d}{dx}[(x-1)^2]\\\\\\\large 0-\dfrac{d}{dx}[(x-1)^2\\\\\\\large using \ identity \ (a-b)^2=a^2+b^2-2ab \ here\\\\\\\large -\dfrac{d}{dx}[(x^2+1-2x)]\\\\\\\large -[2x^{2-1}+0-2x^{1-1}]\\\\\\\\large -[2x-2x^0]\\\\\\\large -2x+2$

Thus we get answer.