Advertisements
Advertisements
प्रश्न
xn tan x
Advertisements
उत्तर
\[\text{ Let } u = x^n ; v = \tan x\]
\[\text{ Then }, u' = n x^{n - 1} ; v' = \sec^2 x\]
\[\text{ Using the product rule }:\]
\[\frac{d}{dx}\left( uv \right) = uv' + vu'\]
\[\frac{d}{dx}\left( x^n \tan x \right) = x^n \sec^2 x + \tan x\left( n x^{n - 1} \right)\]
\[ = x^{n - 1} \left( x \sec^2 x + n \tan x \right)\]
APPEARS IN
संबंधित प्रश्न
Find the derivative of (5x3 + 3x – 1) (x – 1).
Find the derivative of x–3 (5 + 3x).
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 + 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):
cosec x cot x
Find the derivative of the following function at the indicated point:
\[\frac{2}{x}\]
\[\frac{1}{\sqrt{x}}\]
(x + 2)3
\[\sqrt{2 x^2 + 1}\]
x ex
Differentiate each of the following from first principle:
x2 sin x
Differentiate each of the following from first principle:
x2 ex
tan (2x + 1)
\[\sqrt{\tan x}\]
\[\sin \sqrt{2x}\]
\[\cos \sqrt{x}\]
x4 − 2 sin x + 3 cos x
\[\frac{x^3}{3} - 2\sqrt{x} + \frac{5}{x^2}\]
log3 x + 3 loge x + 2 tan x
\[\log\left( \frac{1}{\sqrt{x}} \right) + 5 x^a - 3 a^x + \sqrt[3]{x^2} + 6 \sqrt[4]{x^{- 3}}\]
Find the rate at which the function f (x) = x4 − 2x3 + 3x2 + x + 5 changes with respect to x.
(2x2 − 3) sin x
x−3 (5 + 3x)
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)
\[\frac{x^2 + 1}{x + 1}\]
\[\frac{2x - 1}{x^2 + 1}\]
\[\frac{2^x \cot x}{\sqrt{x}}\]
\[\frac{1 + 3^x}{1 - 3^x}\]
\[\frac{4x + 5 \sin x}{3x + 7 \cos x}\]
\[\frac{a + b \sin x}{c + d \cos x}\]
\[\frac{1}{a x^2 + bx + c}\]
If x < 2, then write the value of \[\frac{d}{dx}(\sqrt{x^2 - 4x + 4)}\]
Write the value of \[\frac{d}{dx}\left( x \left| x \right| \right)\]
Write the derivative of f (x) = 3 |2 + x| at x = −3.
Mark the correct alternative in of the following:
If \[y = \sqrt{x} + \frac{1}{\sqrt{x}}\] then \[\frac{dy}{dx}\] at x = 1 is
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
Mark the correct alternative in of the following:
If\[f\left( x \right) = 1 + x + \frac{x^2}{2} + . . . + \frac{x^{100}}{100}\] then \[f'\left( 1 \right)\] is equal to
