Question

if Y is equal to x square minus x then find DY by DX at x is equal to zero​

Answer 1

AnswEr :

Given,

$\sf \: y = x {}^{2} - x$

To finD : Derivative of y at x = 0

Now,

$\sf \: y' = \dfrac{dy}{dx} \\ \\ \longrightarrow \: \sf \: y' = \dfrac{d( {x}^{2} - x)}{dx} \\ \\ \longrightarrow \: \sf \: y' = \dfrac{ {dx}^{2} }{dx} - \dfrac{dx}{dx} \\ \\ \longrightarrow \: \sf \: y' = 2x - 1$

Thus,derivative of y is 2x - 1

Therefore,

$\implies \sf \: y'(0) = 2(0) - 1 \\ \\ \large{\implies \: \underline{ \boxed{\sf \: y'(0) = - 1}}}$

Thus, derivative of y at x = 0 is - 1