Differentiate from first principles, with respect to x, (3x\(^2\) + 2x - 1)
Question 1 Report
Differentiate from first principles, with respect to x, (3x\(^2\) + 2x - 1)
Answer Details
Let \(f(x)=3x^2+2x-1\). By first principles \(f'(x)=\displaystyle\lim_{h\to 0}\frac{f(x+h)-f(x)}{h}\).
\[f(x+h)=3(x+h)^2+2(x+h)-1=3x^2+6xh+3h^2+2x+2h-1.\] \[f(x+h)-f(x)=6xh+3h^2+2h.\] \[\frac{f(x+h)-f(x)}{h}=6x+3h+2.\] \[f'(x)=\lim_{h\to 0}(6x+3h+2)=6x+2.\]So \(\dfrac{d}{dx}(3x^2+2x-1)=6x+2\).
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