The derivative of fx-x2 isA- xB- 2 xC- x3D- x2-1

The correct option is B 2xf'(x)=lim_h → 0f(x+h) f(x)/h =lim_h → 0(x+h)^2 x^2/h =lim_h → 0(x^2+2xh+h^2) x^2/h =lim_h → 02xh+h^2/h =lim_h → 0 (2x + h) = 2x ...

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Standard XI

Mathematics

Derivative from First Principle

The derivativ...

Question

The derivative of $f (x) = x^{2}$ is .

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x^{3}

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x^{2} + 1

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Solution

The correct option is B 2x
$f^{'} (x) = lim h \to 0 \frac{f (x + h) - f (x)}{h} = lim h \to 0 \frac{(x + h)^{2} - x^{2}}{h} = lim h \to 0 \frac{(x^{2} + 2 x h + h^{2}) - x^{2}}{h} = lim h \to 0 \frac{2 x h + h^{2}}{h} = lim h \to 0 (2 x + h) = 2 x$

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The derivative of f(x)=x2 is .

The correct option is B 2xf′(x)=limh→0f(x+h)−f(x)h=limh→0(x+h)2−x2h=limh→0(x2+2xh+h2)−x2h=limh→02xh+h2h=limh→0(2x+h)=2x

The derivative of $f (x) = x^{2}$ is .

The correct option is B 2x
$f^{'} (x) = lim h \to 0 \frac{f (x + h) - f (x)}{h} = lim h \to 0 \frac{(x + h)^{2} - x^{2}}{h} = lim h \to 0 \frac{(x^{2} + 2 x h + h^{2}) - x^{2}}{h} = lim h \to 0 \frac{2 x h + h^{2}}{h} = lim h \to 0 (2 x + h) = 2 x$