Advertisements
Advertisements
प्रश्न
Find the derivative of the following function at the indicated point:
sin 2x at x =\[\frac{\pi}{2}\]
Advertisements
उत्तर
\[\text{ We have }: \]
\[f'\left( \frac{\pi}{2} \right) = \lim_{h \to 0} \frac{f\left( \frac{\pi}{2} + h \right) - f\left( \frac{\pi}{2} \right)}{h}\]
\[ = \lim_{h \to 0} \frac{\sin2\left( \frac{\pi}{2} + h \right) - \sin2\left( \frac{\pi}{2} \right)}{h}\]
\[ = \lim_{h \to 0} \frac{\sin(\pi + 2h) - 0}{h}\]
\[ = \lim_{h \to 0} \frac{- \sin2h}{h} \times \frac{2}{2} \]
\[ = \lim_{h \to 0} - \frac{\sin 2h}{2h} \times 2 \]
\[ = - 2\]
\[\]
APPEARS IN
संबंधित प्रश्न
Find the derivative of (5x3 + 3x – 1) (x – 1).
Find the derivative of x–4 (3 – 4x–5).
Find the derivative of `2/(x + 1) - x^2/(3x -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):
sin (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):
`cos x/(1 + sin 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):
x4 (5 sin x – 3 cos x)
Find the derivative of f (x) x at x = 1
\[\frac{1}{x^3}\]
\[\frac{1}{\sqrt{3 - x}}\]
(x2 + 1) (x − 5)
\[\frac{2x + 3}{x - 2}\]
Differentiate of the following from first principle:
eax + b
x ex
Differentiate each of the following from first principle:
\[\sqrt{\sin 2x}\]
Differentiate each of the following from first principle:
x2 ex
tan2 x
\[\cos \sqrt{x}\]
x4 − 2 sin x + 3 cos x
\[\frac{2 x^2 + 3x + 4}{x}\]
x3 sin x
(x sin x + cos x ) (ex + x2 log x)
x3 ex cos 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
\[\frac{x^2 + 1}{x + 1}\]
\[\frac{e^x + \sin x}{1 + \log x}\]
\[\frac{x^2 - x + 1}{x^2 + x + 1}\]
\[\frac{1 + 3^x}{1 - 3^x}\]
\[\frac{4x + 5 \sin x}{3x + 7 \cos x}\]
\[\frac{x + \cos x}{\tan x}\]
If \[\frac{\pi}{2}\] then find \[\frac{d}{dx}\left( \sqrt{\frac{1 + \cos 2x}{2}} \right)\]
Write the value of \[\frac{d}{dx}\left( \log \left| x \right| \right)\]
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 \[f'\left( a \right)\]
