Advertisements
Advertisements
प्रश्न
(1 − 2 tan x) (5 + 4 sin x)
उत्तर
\[\text{ Let } u = 1 - 2 \tan x; v = 5 + 4 \sin x \]
\[\text{ Then }, u' = - 2 \sec^2 x; v' = 4 \cos x\]
\[\text{ Using the product rule }:\]
\[\frac{d}{dx}\left( uv \right) = u v' + v u'\]
\[\frac{d}{dx}\left[ \left( 1 - 2 \tan x \right)\left( 5 + 4 \sin x \right) \right]\]
\[ = \left( 1 - 2 \tan x \right)\left( 4 \cos x \right) + \left( 5 + 4 \sin x \right)\left( - 2 \sec^2 x \right)\]
\[ = 4 \cos x - 8 \times \frac{\sin x}{\cos x}\cos x - 10 \sec^2 x - 8 \times \frac{\sin x}{\cos^2 x}\]
\[ = 4 \cos x - 8 \sin x - 10 \sec^2 x - 8 \sec x \tan x \]
\[ = 4\left( \cos x - 2 \sin x - \frac{5}{2} \sec^2 x - 2 \sec x \tan x \right)\]
APPEARS IN
संबंधित प्रश्न
For the function
f(x) = `x^100/100 + x^99/99 + ...+ x^2/2 + x + 1`
Prove that f'(1) = 100 f'(0)
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):
(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):
`(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):
(ax + b)n (cx + d)m
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):
cosec x cot 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 f (x) = 99x at x = 100
\[\frac{x^2 + 1}{x}\]
Differentiate of the following from first principle:
eax + b
Differentiate of the following from first principle:
− x
Differentiate of the following from first principle:
sin (2x − 3)
Differentiate each of the following from first principle:
x2 sin x
Differentiate each of the following from first principle:
\[e^{x^2 + 1}\]
tan2 x
\[\cos \sqrt{x}\]
\[\tan \sqrt{x}\]
ex log a + ea long x + ea log a
\[\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)^3\]
cos (x + a)
\[\text{ If } y = \left( \frac{2 - 3 \cos x}{\sin x} \right), \text{ find } \frac{dy}{dx} at x = \frac{\pi}{4}\]
\[If y = \sqrt{\frac{x}{a}} + \sqrt{\frac{a}{x}}, \text{ prove that } 2xy\frac{dy}{dx} = \left( \frac{x}{a} - \frac{a}{x} \right)\]
x−4 (3 − 4x−5)
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.
(3 sec x − 4 cosec x) (−2 sin x + 5 cos x)
\[\frac{e^x + \sin x}{1 + \log x}\]
\[\frac{x \tan x}{\sec x + \tan x}\]
\[\frac{2^x \cot x}{\sqrt{x}}\]
\[\frac{x^2 - x + 1}{x^2 + x + 1}\]
\[\frac{a + \sin x}{1 + a \sin x}\]
\[\frac{3^x}{x + \tan x}\]
\[\frac{x^5 - \cos x}{\sin x}\]
\[\frac{x + \cos x}{\tan x}\]
\[\frac{1}{a x^2 + bx + c}\]
Write the value of \[\lim_{x \to a} \frac{x f (a) - a f (x)}{x - a}\]
Write the value of the derivative of f (x) = |x − 1| + |x − 3| at x = 2.
Mark the correct alternative in of the following:
If\[f\left( x \right) = 1 - x + x^2 - x^3 + . . . - x^{99} + x^{100}\]then \[f'\left( 1 \right)\]
