Advertisements
Advertisements
Question
Find the derivative of f (x) = x2 − 2 at x = 10
Advertisements
Solution
We have:
\[f'(x) = \lim_{h \to 0} \frac{f(10 + h) - f(10)}{h}\]
\[ = \lim_{h \to 0} \frac{(10 + h )^2 - 2 - ( {10}^2 - 2)}{h}\]
\[ = \lim_{h \to 0} \frac{100 + h^2 + 20h - 2 - 100 + 2}{h}\]
\[ = \lim_{h \to 0} \frac{h^2 + 20h}{h}\]
\[ = \lim_{h \to 0} \frac{h(h + 20)}{h}\]
\[ = \lim_{h \to 0} h + 20\]
\[ = 0 + 20\]
\[ = 20\]
APPEARS IN
RELATED QUESTIONS
Find the derivative of x2 – 2 at x = 10.
Find the derivative of (5x3 + 3x – 1) (x – 1).
Find the derivative of the following function (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
(x + a)
Find the derivative of the following function (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
`4sqrtx - 2`
Find the derivative of the following function (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
cosec x cot x
Find the derivative of the following function (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
`(sin x + cos x)/(sin x - cos x)`
Find the derivative of the following function at the indicated point:
sin 2x at x =\[\frac{\pi}{2}\]
\[\frac{x^2 + 1}{x}\]
\[\frac{x + 1}{x + 2}\]
Differentiate each of the following from first principle:
\[\sqrt{\sin (3x + 1)}\]
Differentiate each of the following from first principle:
x2 ex
tan 2x
\[\tan \sqrt{x}\]
\[\tan \sqrt{x}\]
(2x2 + 1) (3x + 2)
\[\frac{( x^3 + 1)(x - 2)}{x^2}\]
\[\text{ If } y = \left( \frac{2 - 3 \cos x}{\sin x} \right), \text{ find } \frac{dy}{dx} at x = \frac{\pi}{4}\]
xn loga x
(x sin x + cos x ) (ex + x2 log x)
sin2 x
x4 (5 sin x − 3 cos x)
(2x2 − 3) sin x
x5 (3 − 6x−9)
Differentiate each of the following functions by the product rule and the other method and verify that answer from both the methods is the same.
(3x2 + 2)2
Differentiate each of the following functions by the product rule and the other method and verify that answer from both the methods is the same.
(3 sec x − 4 cosec x) (−2 sin x + 5 cos x)
(ax + b) (a + d)2
\[\frac{x^2 + 1}{x + 1}\]
\[\frac{x^2 - x + 1}{x^2 + x + 1}\]
\[\frac{{10}^x}{\sin x}\]
\[\frac{3^x}{x + \tan x}\]
\[\frac{a + b \sin x}{c + d \cos x}\]
\[\frac{p x^2 + qx + r}{ax + b}\]
If f (x) = \[\log_{x_2}\]write the value of f' (x).
Mark the correct alternative in of the following:
If \[y = \frac{1 + \frac{1}{x^2}}{1 - \frac{1}{x^2}}\] then \[\frac{dy}{dx} =\]
Mark the correct alternative in each of the following:
If\[f\left( x \right) = \frac{x^n - a^n}{x - a}\] then \[f'\left( a \right)\]
(ax2 + cot x)(p + q cos x)
