Advertisements
Advertisements
प्रश्न
\[\frac{{10}^x}{\sin x}\]
Advertisements
उत्तर
\[\text{ Let } u = {10}^x ; v = \sin x\]
\[\text{ Then }, u' = {10}^x \log 10; v' = \cos x\]
\[\text{ Using the quotient rule }:\]
\[\frac{d}{dx}\left( \frac{u}{v} \right) = \frac{vu' - uv'}{v^2}\]
\[\frac{d}{dx}\left( \frac{{10}^x}{\sin x} \right) = \frac{\sin x {10}^x \log 10 - {10}^x \cos x}{\sin^2 x}\]
\[ = \frac{\sin x {10}^x \log 10}{\sin^2 x} - \frac{{10}^x \cos x}{\sin^2 x}\]
\[ = {10}^x \log 10 \cos ec x - {10}^x cosec x \cot x\]
\[ = {10}^x cosec x\left( \log 10 - \cot x \right)\]
APPEARS IN
संबंधित प्रश्न
Find the derivative of x2 – 2 at x = 10.
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):
`(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):
`1/(ax^2 + bx + c)`
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 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):
`cos x/(1 + sin x)`
Find the derivative of the following function at the indicated point:
sin x at x =\[\frac{\pi}{2}\]
\[\frac{2}{x}\]
\[\frac{1}{\sqrt{x}}\]
k xn
x2 + x + 3
(x2 + 1) (x − 5)
Differentiate each of the following from first principle:
e−x
Differentiate of the following from first principle:
x sin x
Differentiate each of the following from first principle:
x2 sin x
Differentiate each of the following from first principle:
\[\sqrt{\sin (3x + 1)}\]
Differentiate each of the following from first principle:
\[e^{x^2 + 1}\]
Differentiate each of the following from first principle:
\[e^\sqrt{2x}\]
tan2 x
ex log a + ea long x + ea log a
\[\frac{( x^3 + 1)(x - 2)}{x^2}\]
cos (x + a)
\[\text{ If } y = \left( \frac{2 - 3 \cos x}{\sin x} \right), \text{ find } \frac{dy}{dx} at x = \frac{\pi}{4}\]
\[\text{ If } y = \frac{2 x^9}{3} - \frac{5}{7} x^7 + 6 x^3 - x, \text{ find } \frac{dy}{dx} at x = 1 .\]
(x sin x + cos x) (x cos x − sin x)
sin2 x
\[\frac{x^2 + 1}{x + 1}\]
\[\frac{e^x - \tan x}{\cot x - x^n}\]
\[\frac{e^x + \sin x}{1 + \log x}\]
\[\frac{x \tan x}{\sec x + \tan x}\]
\[\frac{\sin x - x \cos x}{x \sin x + \cos x}\]
\[\frac{x^5 - \cos x}{\sin x}\]
Write the value of \[\lim_{x \to a} \frac{x f (a) - a f (x)}{x - a}\]
If \[\frac{\pi}{2}\] then find \[\frac{d}{dx}\left( \sqrt{\frac{1 + \cos 2x}{2}} \right)\]
Mark the correct alternative in of the following:
If \[f\left( x \right) = x^{100} + x^{99} + . . . + x + 1\] then \[f'\left( 1 \right)\] is equal to
Let f(x) = x – [x]; ∈ R, then f'`(1/2)` is ______.
