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 `2x - 3/4`
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):
(ax + b) (cx + d)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):
`1/(ax^2 + bx + c)`
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):
`a/x^4 = b/x^2 + cos 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):
`(sec x - 1)/(sec x + 1)`
Find the derivative of the following function at the indicated point:
\[\frac{1}{\sqrt{x}}\]
\[\frac{x^2 + 1}{x}\]
\[\frac{2x + 3}{x - 2}\]
Differentiate of the following from first principle:
− x
Differentiate of the following from first principle:
\[\cos\left( x - \frac{\pi}{8} \right)\]
Differentiate of the following from first principle:
x cos x
Differentiate each of the following from first principle:
\[\frac{\cos x}{x}\]
Differentiate each of the following from first principle:
\[e^\sqrt{2x}\]
x4 − 2 sin x + 3 cos x
ex log a + ea long x + ea log a
(2x2 + 1) (3x + 2)
2 sec x + 3 cot x − 4 tan x
a0 xn + a1 xn−1 + a2 xn−2 + ... + an−1 x + an.
xn loga x
\[\frac{x^2 \cos\frac{\pi}{4}}{\sin x}\]
(2x2 − 3) sin x
(ax + b) (a + d)2
\[\frac{2x - 1}{x^2 + 1}\]
\[\frac{e^x}{1 + x^2}\]
\[\frac{e^x + \sin x}{1 + \log x}\]
\[\frac{x \sin x}{1 + \cos x}\]
\[\frac{2^x \cot x}{\sqrt{x}}\]
\[\frac{1 + 3^x}{1 - 3^x}\]
\[\frac{1 + \log x}{1 - \log x}\]
\[\frac{a + b \sin x}{c + d \cos x}\]
\[\frac{p x^2 + qx + r}{ax + b}\]
\[\frac{x^5 - \cos x}{\sin x}\]
Mark the correct alternative in of the following:
Let f(x) = x − [x], x ∈ R, then \[f'\left( \frac{1}{2} \right)\]
Mark the correct alternative in of the following:
If\[f\left( x \right) = 1 + x + \frac{x^2}{2} + . . . + \frac{x^{100}}{100}\] then \[f'\left( 1 \right)\] is equal to
(ax2 + cot x)(p + q cos x)
