Advertisements
Advertisements
Question
(1 − 2 tan x) (5 + 4 sin x)
Advertisements
Solution
\[\text{ Let } u = 1 - 2 \tan x; v = 5 + 4 \sin x \]
\[\text{ Then }, u' = - 2 \sec^2 x; v' = 4 \cos x\]
\[\text{ Using the product rule }:\]
\[\frac{d}{dx}\left( uv \right) = u v' + v u'\]
\[\frac{d}{dx}\left[ \left( 1 - 2 \tan x \right)\left( 5 + 4 \sin x \right) \right]\]
\[ = \left( 1 - 2 \tan x \right)\left( 4 \cos x \right) + \left( 5 + 4 \sin x \right)\left( - 2 \sec^2 x \right)\]
\[ = 4 \cos x - 8 \times \frac{\sin x}{\cos x}\cos x - 10 \sec^2 x - 8 \times \frac{\sin x}{\cos^2 x}\]
\[ = 4 \cos x - 8 \sin x - 10 \sec^2 x - 8 \sec x \tan x \]
\[ = 4\left( \cos x - 2 \sin x - \frac{5}{2} \sec^2 x - 2 \sec x \tan x \right)\]
APPEARS IN
RELATED QUESTIONS
Find the derivative of x2 – 2 at x = 10.
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):
sinn x
Find the derivative of the following function at the indicated point:
sin x at x =\[\frac{\pi}{2}\]
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 =\[\frac{\pi}{2}\]
\[\frac{1}{\sqrt{x}}\]
Differentiate each of the following from first principle:
\[\sqrt{\sin 2x}\]
Differentiate each of the following from first principle:
\[\frac{\cos x}{x}\]
Differentiate each of the following from first principle:
x2 sin x
Differentiate each of the following from first principle:
\[a^\sqrt{x}\]
\[\sqrt{\tan x}\]
\[\tan \sqrt{x}\]
x4 − 2 sin x + 3 cos x
3x + x3 + 33
ex log a + ea long x + ea log a
\[\frac{1}{\sin x} + 2^{x + 3} + \frac{4}{\log_x 3}\]
\[\text{ If } y = \frac{2 x^9}{3} - \frac{5}{7} x^7 + 6 x^3 - x, \text{ find } \frac{dy}{dx} at x = 1 .\]
If for f (x) = λ x2 + μ x + 12, f' (4) = 15 and f' (2) = 11, then find λ and μ.
(x3 + x2 + 1) sin x
x5 ex + x6 log x
(x sin x + cos x) (x cos x − sin x)
x5 (3 − 6x−9)
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.
(3x2 + 2)2
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)
\[\frac{\sqrt{a} + \sqrt{x}}{\sqrt{a} - \sqrt{x}}\]
\[\frac{1 + 3^x}{1 - 3^x}\]
\[\frac{x^5 - \cos x}{\sin x}\]
\[\frac{ax + b}{p x^2 + qx + r}\]
Mark the correct alternative in of the following:
Let f(x) = x − [x], x ∈ R, then \[f'\left( \frac{1}{2} \right)\]
Mark the correct alternative in of the following:
If \[y = \sqrt{x} + \frac{1}{\sqrt{x}}\] then \[\frac{dy}{dx}\] at x = 1 is
(ax2 + cot x)(p + q cos x)
`(a + b sin x)/(c + d cos x)`
