Advertisements
Advertisements
प्रश्न
x3 ex
उत्तर
\[\text{ Let } u = x^3 ; v = e^x \]
\[\text{ Then }, u' = 3 x^2 ; v' = e^x \]
\[\text{ Using the product rule }:\]
\[\frac{d}{dx}\left( uv \right) = uv' + vu'\]
\[\frac{d}{dx}\left( x^3 e^x \right) = x^3 e^x + e^x \left( 3 x^2 \right)\]
\[ = x^2 e^x \left( x + 3 \right)\]
APPEARS IN
संबंधित प्रश्न
For the function
f(x) = `x^100/100 + x^99/99 + ...+ x^2/2 + x + 1`
Prove that f'(1) = 100 f'(0)
Find the derivative of `2x - 3/4`
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):
`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):
`(a + bsin x)/(c + dcosx)`
Find the derivative of f (x) = 3x at x = 2
Find the derivative of f (x) x at x = 1
Find the derivative of the following function at the indicated point:
\[\frac{2}{x}\]
\[\frac{1}{\sqrt{x}}\]
\[\frac{x + 1}{x + 2}\]
(x2 + 1) (x − 5)
\[\frac{2x + 3}{x - 2}\]
Differentiate each of the following from first principle:
e−x
Differentiate of the following from first principle:
x cos x
Differentiate each of the following from first principle:
\[e^\sqrt{2x}\]
Differentiate each of the following from first principle:
\[a^\sqrt{x}\]
\[\frac{x^3}{3} - 2\sqrt{x} + \frac{5}{x^2}\]
ex log a + ea long x + ea log a
\[\left( x + \frac{1}{x} \right)\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)\]
For the function \[f(x) = \frac{x^{100}}{100} + \frac{x^{99}}{99} + . . . + \frac{x^2}{2} + x + 1 .\]
x2 sin x log x
x5 ex + x6 log x
(x sin x + cos x) (x cos x − sin x)
\[\frac{x^2 \cos\frac{\pi}{4}}{\sin x}\]
x5 (3 − 6x−9)
x−4 (3 − 4x−5)
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)
(ax + b) (a + d)2
\[\frac{x}{1 + \tan x}\]
\[\frac{x \tan x}{\sec x + \tan x}\]
\[\frac{\sin x - x \cos x}{x \sin x + \cos x}\]
\[\frac{a + \sin x}{1 + a \sin x}\]
\[\frac{x^5 - \cos x}{\sin x}\]
If \[\frac{\pi}{2}\] then find \[\frac{d}{dx}\left( \sqrt{\frac{1 + \cos 2x}{2}} \right)\]
If |x| < 1 and y = 1 + x + x2 + x3 + ..., then write the value of \[\frac{dy}{dx}\]
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 each of the following:
If\[y = \frac{\sin x + \cos x}{\sin x - \cos x}\] then \[\frac{dy}{dx}\]at x = 0 is
