Advertisements
Advertisements
प्रश्न
Find the derivative of the following function at the indicated point:
2 cos x at x =\[\frac{\pi}{2}\]
Advertisements
उत्तर
\[\text{ We have }: \]
\[f'\left( \frac{\pi}{2} \right) = \lim_{h \to 0} \frac{f\left( \frac{\pi}{2} + h \right) - f\left( \frac{\pi}{2} \right)}{h}\]
\[ = \lim_{h \to 0} \frac{2cos\left( \frac{\pi}{2} + h \right) - cos\left( \frac{\pi}{2} \right)}{h}\]
\[ = \lim_{h \to 0} \frac{- 2sin h - 0}{h}\]
\[ = - 2 \lim_{h \to 0} \frac{\sinh}{h}\]
\[ = - 2(1)\]
\[ = - 2\]
APPEARS IN
संबंधित प्रश्न
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):
`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):
`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):
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):
`(sin x + cos x)/(sin x - 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):
sinn x
Find the derivative of f (x) = 3x at x = 2
\[\frac{1}{\sqrt{x}}\]
\[\frac{x^2 + 1}{x}\]
(x2 + 1) (x − 5)
\[\frac{2x + 3}{x - 2}\]
Differentiate of the following from first principle:
x sin x
Differentiate of the following from first principle:
x cos x
\[\cos \sqrt{x}\]
\[\tan \sqrt{x}\]
\[\tan \sqrt{x}\]
cos (x + a)
Find the rate at which the function f (x) = x4 − 2x3 + 3x2 + x + 5 changes with respect to x.
\[\text{ If } y = \frac{2 x^9}{3} - \frac{5}{7} x^7 + 6 x^3 - x, \text{ find } \frac{dy}{dx} at x = 1 .\]
(x3 + x2 + 1) sin x
x2 sin x log x
\[e^x \log \sqrt{x} \tan x\]
(ax + b)n (cx + d)n
\[\frac{\sqrt{a} + \sqrt{x}}{\sqrt{a} - \sqrt{x}}\]
\[\frac{{10}^x}{\sin x}\]
\[\frac{1 + 3^x}{1 - 3^x}\]
\[\frac{4x + 5 \sin x}{3x + 7 \cos x}\]
\[\frac{a + b \sin x}{c + d \cos x}\]
\[\frac{x + \cos x}{\tan x}\]
\[\frac{x}{\sin^n x}\]
If \[\frac{\pi}{2}\] then find \[\frac{d}{dx}\left( \sqrt{\frac{1 + \cos 2x}{2}} \right)\]
If |x| < 1 and y = 1 + x + x2 + x3 + ..., then write the value of \[\frac{dy}{dx}\]
If f (x) = \[\log_{x_2}\]write the value of f' (x).
Mark the correct alternative in of the following:
If \[f\left( x \right) = x^{100} + x^{99} + . . . + x + 1\] then \[f'\left( 1 \right)\] is equal to
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
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
Find the derivative of f(x) = tan(ax + b), by first principle.
(ax2 + cot x)(p + q cos x)
