Advertisements
Advertisements
प्रश्न
cos (x + a)
Advertisements
उत्तर
\[\frac{d}{dx}\left[ \cos \left( x + a \right) \right]\]
\[ = \frac{d}{dx}\left( \cos x \cos a - \sin x \sin a \right)\]
\[ = \cos a\frac{d}{dx}\left( \cos x \right) - \sin a \frac{d}{dx}\left( \sin x \right)\]
\[ = - \cos a \sin x - \sin a \cos x\]
\[ = - \left( \sin x \cos a + \cos x \sin a \right)\]
\[ = - \sin\left( x + a \right)\]
APPEARS IN
संबंधित प्रश्न
Find the derivative of x–3 (5 + 3x).
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)`
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 + 1/x)/(1- 1/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 + a)
Find the derivative of f (x) = 99x at x = 100
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 =\[\frac{\pi}{2}\]
\[\frac{x^2 - 1}{x}\]
k xn
(x + 2)3
Differentiate of the following from first principle:
sin (x + 1)
Differentiate each of the following from first principle:
\[\frac{\cos x}{x}\]
\[\cos \sqrt{x}\]
\[\tan \sqrt{x}\]
ex log a + ea long x + ea log a
log3 x + 3 loge x + 2 tan x
\[\frac{2 x^2 + 3x + 4}{x}\]
\[\frac{a \cos x + b \sin x + c}{\sin x}\]
a0 xn + a1 xn−1 + a2 xn−2 + ... + an−1 x + an.
Find the rate at which the function f (x) = x4 − 2x3 + 3x2 + x + 5 changes with respect to x.
xn loga x
(x3 + x2 + 1) sin x
(x sin x + cos x ) (ex + x2 log x)
(2x2 − 3) sin 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)
(ax + b) (a + d)2
\[\frac{x^2 + 1}{x + 1}\]
\[\frac{e^x - \tan x}{\cot x - x^n}\]
\[\frac{x \sin x}{1 + \cos x}\]
\[\frac{2^x \cot x}{\sqrt{x}}\]
\[\frac{\sin x - x \cos x}{x \sin x + \cos x}\]
\[\frac{{10}^x}{\sin x}\]
\[\frac{1 + 3^x}{1 - 3^x}\]
\[\frac{p x^2 + qx + r}{ax + b}\]
\[\frac{x^5 - \cos x}{\sin x}\]
Write the value of \[\lim_{x \to c} \frac{f(x) - f(c)}{x - c}\]
If f (1) = 1, f' (1) = 2, then write the value of \[\lim_{x \to 1} \frac{\sqrt{f (x)} - 1}{\sqrt{x} - 1}\]
If f (x) = \[\log_{x_2}\]write the value of f' (x).
