Advertisements
Advertisements
प्रश्न
(1 − 2 tan x) (5 + 4 sin x)
Advertisements
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
Find the derivative of (5x3 + 3x – 1) (x – 1).
Find the derivative of x5 (3 – 6x–9).
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):
`(px^2 +qx + r)/(ax +b)`
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/x^4 = b/x^2 + 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):
`(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):
`(a + bsin x)/(c + dcosx)`
Find the derivative of f (x) = cos x at x = 0
Find the derivative of the following function at the indicated point:
sin 2x at x =\[\frac{\pi}{2}\]
\[\frac{1}{x^3}\]
\[\frac{x + 1}{x + 2}\]
\[\frac{x + 2}{3x + 5}\]
\[\sqrt{2 x^2 + 1}\]
\[\frac{2x + 3}{x - 2}\]
Differentiate each of the following from first principle:
e−x
Differentiate of the following from first principle:
sin (2x − 3)
Differentiate each of the following from first principle:
\[e^{x^2 + 1}\]
x4 − 2 sin x + 3 cos x
\[\frac{( x^3 + 1)(x - 2)}{x^2}\]
x2 sin x log x
\[\frac{x^2 \cos\frac{\pi}{4}}{\sin x}\]
\[\frac{x}{1 + \tan x}\]
\[\frac{e^x}{1 + x^2}\]
\[\frac{\sqrt{a} + \sqrt{x}}{\sqrt{a} - \sqrt{x}}\]
\[\frac{a + \sin x}{1 + a \sin x}\]
\[\frac{{10}^x}{\sin x}\]
\[\frac{1 + 3^x}{1 - 3^x}\]
If x < 2, then write the value of \[\frac{d}{dx}(\sqrt{x^2 - 4x + 4)}\]
If f (x) = \[\frac{x^2}{\left| x \right|},\text{ write }\frac{d}{dx}\left( f (x) \right)\]
If f (x) = |x| + |x−1|, write the value of \[\frac{d}{dx}\left( f (x) \right)\]
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 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 2x4 + x.
Find the derivative of x2 cosx.
Find the derivative of f(x) = tan(ax + b), by first principle.
(ax2 + cot x)(p + q cos x)
Let f(x) = x – [x]; ∈ R, then f'`(1/2)` is ______.
