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Find the derivative of the following with respect to x using first principles. Find the values of the following limits.

September 8, 2026Mathematics

ScanSolve AI Answer

Answer

2x - 1

3 steps

Identify the function to be differentiated.
The given function is $F(x) = x^2 - x$ .
Apply the power rule for differentiation.
The power rule states that $\frac{d}{dx}(x^n) = nx^{n-1}$ .
For the term $x^2$ , the derivative is $2x^{2-1} = 2x$ .
For the term $x$ , which is $x^1$ , the derivative is $1x^{1-1} = 1x^0 = 1$ .
Combine the derivatives of each term.
The derivative of $F(x)$ is the derivative of $x^2$ minus the derivative of $x$ .
$F'(x) = \frac{d}{dx}(x^2) - \frac{d}{dx}(x)$ $F'(x) = 2x - 1$
The derivative of $F(x)$ is $\boxed{2x - 1}$ .

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