Advertisements
Advertisements
प्रश्न
\[\frac{e^x - \tan x}{\cot x - x^n}\]
उत्तर
\[\text{ Let } u = e^x - \tan x; v = \cot x - x^n \]
\[\text{ Then }, u' = e^x - \sec^2 x; v' = - \cos e c^2 x - n x^{n - 1} \]
\[\text{ Using the quotient rule }:\]
\[\frac{d}{dx}\left( \frac{u}{v} \right) = \frac{vu' - uv'}{v^2}\]
\[\frac{d}{dx}\left( \frac{e^x - \tan x}{cot x - x^n} \right) = \frac{\left( \cot x - x^n \right)\left( e^x - \sec^2 x \right) - \left( e^x - \tan x \right)\left( - \cos e c^2 x - n x^{n - 1} \right)}{\left( \cot x - x^n \right)^2}\]
\[ = \frac{\left( \cot x - x^n \right)\left( e^x - \sec^2 x \right) + \left( e^x - \tan x \right)\left( \cos e c^2 x + n x^{n - 1} \right)}{\left( \cot x - x^n \right)^2}\]
APPEARS IN
संबंधित प्रश्न
Find the derivative of `2/(x + 1) - x^2/(3x -1)`.
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+ q) (r/s + s)`
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):
`(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):
`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):
(ax + b)n
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 f (x) = cos x at x = 0
Find the derivative of the following function at the indicated point:
2 cos x at x =\[\frac{\pi}{2}\]
\[\frac{2}{x}\]
\[\frac{1}{x^3}\]
x ex
Differentiate of the following from first principle:
x sin x
Differentiate each of the following from first principle:
\[\frac{\sin x}{x}\]
Differentiate each of the following from first principle:
\[\frac{\cos x}{x}\]
Differentiate each of the following from first principle:
\[e^\sqrt{2x}\]
Differentiate each of the following from first principle:
\[e^\sqrt{ax + b}\]
Differentiate each of the following from first principle:
\[a^\sqrt{x}\]
tan2 x
\[\sqrt{\tan x}\]
log3 x + 3 loge x + 2 tan x
xn loga x
\[\frac{2^x \cot x}{\sqrt{x}}\]
(1 +x2) cos x
x3 ex cos x
\[\frac{x + e^x}{1 + \log x}\]
\[\frac{\sqrt{a} + \sqrt{x}}{\sqrt{a} - \sqrt{x}}\]
\[\frac{x}{1 + \tan x}\]
\[\frac{\sec x - 1}{\sec x + 1}\]
\[\frac{x^5 - \cos x}{\sin x}\]
\[\frac{x}{\sin^n x}\]
\[\frac{ax + b}{p x^2 + qx + r}\]
Write the value of \[\lim_{x \to a} \frac{x f (a) - a f (x)}{x - a}\]
If \[\frac{\pi}{2}\] then find \[\frac{d}{dx}\left( \sqrt{\frac{1 + \cos 2x}{2}} \right)\]
If f (1) = 1, f' (1) = 2, then write the value of \[\lim_{x \to 1} \frac{\sqrt{f (x)} - 1}{\sqrt{x} - 1}\]
Write the derivative of f (x) = 3 |2 + x| at x = −3.
Mark the correct alternative in of the following:
Let f(x) = x − [x], x ∈ R, then \[f'\left( \frac{1}{2} \right)\]
