Question

What is the derivative of x^2-x+3 at the point x=5

Answer 1

Answer:

Step-by-step explanation:

From given

=d/dx(x^2-x+3)

= 2x-1

X=1/2

From given the derivative of x^2-x+3 at x=5 is

=10-1

9

Answer 2

Question :-

What is the derivative of x² - x + 3 at the point

x = 5 .

Answer :-

$\to \boxed{ \sf \frac{dy}{dx} \bigg |_{x = 5} \: = 9} \:$

Solution :-

We have and let ,

$\longmapsto \sf \: y = {x}^{2} - x + 3 = 0 \\ \\ \sf differentiate \: with \: respect \: to \: x \\ \\ \to \sf \frac{dy}{dx} = \frac{d}{dx} {x}^{2} - \frac{d}{dx} x + \frac{d}{dx} 3 \\ \\ \boxed{ \because \sf\frac{d}{dx} {x}^{n} = n {x}^{n - 1} \: and \: \frac{d}{dx} \: constant = 0} \\ \\ \to \sf \frac{dy}{dx} = 2x - 1 + 0 \\ \bf hence \\ \\ \to \sf \frac{dy}{dx} \bigg |_{x = 5} \: = 2 \times 5- 1 \\ \\ \to \: \sf \frac{dy}{dx} \bigg |_{x = 5} \: = 10 - 1 \\ \\ \to \boxed{ \sf \frac{dy}{dx} \bigg |_{x = 5} \: = 9}$