Advertisements
Advertisements
Question
Find the derivative of f (x) = x2 − 2 at x = 10
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 (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):
(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):
sinn 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):
`(a + bsin x)/(c + dcosx)`
Find the derivative of the following function at the indicated point:
Find the derivative of the following function at the indicated point:
2 cos x at x =\[\frac{\pi}{2}\]
Find the derivative of the following function at the indicated point:
sin 2x at x =\[\frac{\pi}{2}\]
\[\frac{2}{x}\]
\[\frac{1}{\sqrt{x}}\]
\[\frac{1}{x^3}\]
\[\frac{x^2 - 1}{x}\]
\[\frac{x + 1}{x + 2}\]
Differentiate of the following from first principle:
eax + b
Differentiate each of the following from first principle:
\[\frac{\cos x}{x}\]
Differentiate each of the following from first principle:
\[e^\sqrt{2x}\]
Differentiate each of the following from first principle:
\[a^\sqrt{x}\]
\[\cos \sqrt{x}\]
(2x2 + 1) (3x + 2)
\[\left( x + \frac{1}{x} \right)\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)\]
\[\frac{1}{\sin x} + 2^{x + 3} + \frac{4}{\log_x 3}\]
\[\log\left( \frac{1}{\sqrt{x}} \right) + 5 x^a - 3 a^x + \sqrt[3]{x^2} + 6 \sqrt[4]{x^{- 3}}\]
\[\text{ If } y = \left( \sin\frac{x}{2} + \cos\frac{x}{2} \right)^2 , \text{ find } \frac{dy}{dx} at x = \frac{\pi}{6} .\]
Find the slope of the tangent to the curve f (x) = 2x6 + x4 − 1 at x = 1.
If for f (x) = λ x2 + μ x + 12, f' (4) = 15 and f' (2) = 11, then find λ and μ.
x3 ex
x2 sin x log x
\[e^x \log \sqrt{x} \tan x\]
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.
(x + 2) (x + 3)
\[\frac{a x^2 + bx + c}{p x^2 + qx + r}\]
\[\frac{x \sin x}{1 + \cos x}\]
\[\frac{a + \sin x}{1 + a \sin x}\]
\[\frac{{10}^x}{\sin x}\]
\[\frac{a + b \sin x}{c + d \cos x}\]
\[\frac{1}{a x^2 + bx + c}\]
Write the value of \[\frac{d}{dx}\left( x \left| x \right| \right)\]
If f (x) = \[\log_{x_2}\]write the value of f' (x).
Mark the correct alternative in each of the following:
If\[y = \frac{\sin x + \cos x}{\sin x - \cos x}\] then \[\frac{dy}{dx}\]at x = 0 is
Let f(x) = x – [x]; ∈ R, then f'`(1/2)` is ______.
