(A) Let $f(x) = (x-a)(x-b)$.Expanding the expression,we get:$f(x) = x^2 - ax - bx + ab = x^2 - (a+b)x + ab$.Now,differentiate with respect to $x$:$f'(

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(A) Let $f(x) = (x-a)(x-b)$.Expanding the expression,we get:$f(x) = x^2 - ax - bx + ab = x^2 - (a+b)x + ab$.Now,differentiate with respect to $x$:$f'(x) = \frac{d}{dx}(x^2 - (a+b)x + ab)$.Using the power rule $\frac{d}{dx}(x^n) = nx^{n-1}$ and the fact that the derivative of a constant is $0$:$f'(x) = 2x - (a+b) + 0$.Therefore,$f'(x) = 2x - a - b$.

Class 12 Mathematics Continuity and Differentiation Derivative at a point, Standard differentiation

Medium

For some constants $a$ and $b$,find the derivative of $(x-a)(x-b)$.

A
$2x - a - b$
B
$2x + a + b$
C
$x - a - b$
D
$2x - a + b$

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