Find the derivative of f(x) from the first principle of where i(x) = tan x + sec x.

(ii) Evaluate $l i m_{x \to a} \frac{(x + 2)^{\frac{3}{2}} - (a + 2)^{\frac{3}{2}}}{x - a}$

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Solution

(i) $f^{'} (x) = s e c^{2} x + s e c x t a n x$ (ii) $\frac{3}{2} \sqrt{a + 2}$

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Similar questions

(i) If $f (x) = {\begin{matrix} \frac{x - | x |}{x} & i f x \neq 0 2 & i f x = 0 \end{matrix}$ , show that $l i m x \to 0 f (x)$ does not exist.

(ii) Evaluate $l i m x \to 0 \frac{s i n x - 2 x i n 3 x + s i n 5 x}{x} .$

(i) Find the derivative of $\frac{(x - 1) (x - 2)}{(x - 3) (x - 4)} .$

(ii) Differentiate $x e^{x}$ by using first principle.

l i m x \to a \frac{{(x + 2)}^{3 / 2} - {(a + 2)}^{3 / 2}}{x - a}

(i) Evaluate ${lim}_{x \to 1} \frac{x + x^{2} + x^{3} + . . . + x^{n} - n}{x - 1}$

(ii) Find the derivative $\sqrt{sin x}$ from first principle.

lim x \to a \frac{(x + 2)^{3 / 2} - (a + 2)^{3 / 2}}{x - a}

${lim}_{x \to a} \frac{(x + 2)^{\frac{3}{2}} - (a + 2)^{\frac{3}{2}}}{x - a}$

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