Advertisements
Advertisements
प्रश्न
\[\frac{x}{\sin^n x}\]
Advertisements
उत्तर
\[\text{ Let } u = x; v = \sin^n x\]
\[\text{ Then }, u' = 1; v' = n \sin^{n - 1} x . \cos x\]
\[\text{ Using the quotient rule }:\]
\[\frac{d}{dx}\left( \frac{u}{v} \right) = \frac{vu' - uv'}{v^2}\]
\[\frac{d}{dx}\left( \frac{x}{\sin^n x} \right) = \frac{\sin^n x . 1 - x n \sin^{n - 1} x . \cos x}{\left( \sin^n x \right)^2}\]
\[ = \frac{\sin^{n - 1} x\left( \sin x - nx . \cos x \right)}{\sin^{2n} x}\]
\[ = \frac{\sin x - nx . \cos x}{\sin^{2n - \left( n - 1 \right)} x}\]
\[ = \frac{\sin x - nx\cos x}{\sin^{n + 1} x}\]
APPEARS IN
संबंधित प्रश्न
Find the derivative of x–4 (3 – 4x–5).
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):
(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):
`(sec x - 1)/(sec x + 1)`
Find the derivative of f (x) = x2 − 2 at x = 10
Find the derivative of f (x) = cos x at x = 0
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:
\[\frac{1}{x^3}\]
\[\frac{x^2 - 1}{x}\]
\[\frac{x + 2}{3x + 5}\]
(x + 2)3
\[\frac{2x + 3}{x - 2}\]
x ex
Differentiate of the following from first principle:
(−x)−1
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:
sin x + cos x
Differentiate each of the following from first principle:
\[e^\sqrt{ax + b}\]
tan 2x
\[\tan \sqrt{x}\]
\[\tan \sqrt{x}\]
\[\frac{1}{\sin x} + 2^{x + 3} + \frac{4}{\log_x 3}\]
If for f (x) = λ x2 + μ x + 12, f' (4) = 15 and f' (2) = 11, then find λ and μ.
xn tan x
xn loga x
sin x cos x
\[\frac{2^x \cot x}{\sqrt{x}}\]
\[\frac{x}{1 + \tan x}\]
\[\frac{\sin x - x \cos x}{x \sin x + \cos x}\]
\[\frac{a + \sin x}{1 + a \sin x}\]
\[\frac{1 + \log x}{1 - \log x}\]
If f (x) = \[\log_{x_2}\]write the value of f' (x).
Mark the correct alternative in of the following:
If\[y = 1 + \frac{x}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + . . .\]then \[\frac{dy}{dx} =\]
Mark the correct alternative in of the following:
If \[y = \frac{1 + \frac{1}{x^2}}{1 - \frac{1}{x^2}}\] then \[\frac{dy}{dx} =\]
Mark the correct alternative in of the following:
If \[y = \sqrt{x} + \frac{1}{\sqrt{x}}\] then \[\frac{dy}{dx}\] at x = 1 is
Find the derivative of f(x) = tan(ax + b), by first principle.
Let f(x) = x – [x]; ∈ R, then f'`(1/2)` is ______.
