Advertisements
Advertisements
प्रश्न
a0 xn + a1 xn−1 + a2 xn−2 + ... + an−1 x + an.
उत्तर
\[\frac{d}{dx}\left[ \left( a_0 x^n \right) + \frac{d}{dx}\left( a_1 x^{n - 1} \right) + \frac{d}{dx}\left( a_2 x^{n - 2} \right) + . . . + a_{n - 1} x + a_n \right]\]
\[ = a_0 \frac{d}{dx}\left( x^n \right) + a_1 \frac{d}{dx}\left( x^{n - 1} \right) + a_2 \frac{d}{dx}\left( x^{n - 2} \right) + . . . + a_{n - 1} \frac{d}{dx}\left( x \right) + \frac{d}{dx}\left( a_n \right)\]
\[ = n a_0 x^{n - 1} + \left( n - 1 \right) a_1 x^{n - 2} + \left( n - 2 \right) a_2 x^{n - 3} + . . . . + a_{n - 1} \left( 1 \right) + 0\]
\[ = n a_0 x^{n - 1} + \left( n - 1 \right) a_1 x^{n - 2} + \left( n - 2 \right) a_2 x^{n - 3} + . . . . + a_{n - 1} \]
\[\]
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^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):
(ax + b)n (cx + d)m
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 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))/ cos x`
Find the derivative of f (x) x at x = 1
Find the derivative of f (x) = tan x at x = 0
Find the derivative of the following function at the indicated point:
2 cos x at x =\[\frac{\pi}{2}\]
\[\frac{1}{\sqrt{x}}\]
k xn
Differentiate each of the following from first principle:
\[\frac{\cos x}{x}\]
Differentiate each of the following from first principle:
\[e^{x^2 + 1}\]
tan 2x
(2x2 + 1) (3x + 2)
\[\frac{( x^3 + 1)(x - 2)}{x^2}\]
\[\frac{1}{\sin x} + 2^{x + 3} + \frac{4}{\log_x 3}\]
\[\text{ If } y = \left( \sin\frac{x}{2} + \cos\frac{x}{2} \right)^2 , \text{ find } \frac{dy}{dx} at x = \frac{\pi}{6} .\]
Find the rate at which the function f (x) = x4 − 2x3 + 3x2 + x + 5 changes with respect to x.
x3 ex
sin x cos x
(1 − 2 tan x) (5 + 4 sin x)
\[\frac{x^2 \cos\frac{\pi}{4}}{\sin x}\]
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.
(3x2 + 2)2
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.
(3 sec x − 4 cosec x) (−2 sin x + 5 cos x)
\[\frac{e^x - \tan x}{\cot x - x^n}\]
\[\frac{x}{1 + \tan x}\]
\[\frac{x \tan x}{\sec x + \tan x}\]
\[\frac{2^x \cot x}{\sqrt{x}}\]
\[\frac{a + b \sin x}{c + d \cos x}\]
\[\frac{x^5 - \cos x}{\sin x}\]
Write the derivative of f (x) = 3 |2 + x| at x = −3.
If f (x) = \[\log_{x_2}\]write the value of f' (x).
Mark the correct alternative in each of the following:
If\[f\left( x \right) = \frac{x^n - a^n}{x - a}\] then \[f'\left( a \right)\]
(ax2 + cot x)(p + q cos x)
