Advertisements
Advertisements
प्रश्न
a0 xn + a1 xn−1 + a2 xn−2 + ... + an−1 x + an.
Advertisements
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
Find the derivative of (5x3 + 3x – 1) (x – 1).
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) (cx + d)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):
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):
`(a + bsin x)/(c + dcosx)`
Find the derivative of f (x) = 3x at x = 2
Find the derivative of the following function at the indicated point:
sin x at x =\[\frac{\pi}{2}\]
\[\frac{2}{x}\]
\[\frac{1}{x^3}\]
Differentiate each of the following from first principle:
e−x
Differentiate of the following from first principle:
e3x
Differentiate each of the following from first principle:
x2 sin x
Differentiate each of the following from first principle:
\[e^{x^2 + 1}\]
Differentiate each of the following from first principle:
\[e^\sqrt{2x}\]
tan 2x
ex log a + ea long x + ea log a
\[\left( x + \frac{1}{x} \right)\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)\]
\[\frac{( x^3 + 1)(x - 2)}{x^2}\]
\[\frac{a \cos x + b \sin x + c}{\sin x}\]
\[\frac{(x + 5)(2 x^2 - 1)}{x}\]
\[\text{ If } y = \frac{2 x^9}{3} - \frac{5}{7} x^7 + 6 x^3 - x, \text{ find } \frac{dy}{dx} at x = 1 .\]
xn loga x
x3 ex cos 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.
(3 sec x − 4 cosec x) (−2 sin x + 5 cos x)
(ax + b)n (cx + d)n
\[\frac{x \sin x}{1 + \cos x}\]
\[\frac{\sin x - x \cos x}{x \sin x + \cos x}\]
\[\frac{\sqrt{a} + \sqrt{x}}{\sqrt{a} - \sqrt{x}}\]
\[\frac{{10}^x}{\sin x}\]
\[\frac{p x^2 + qx + r}{ax + b}\]
\[\frac{x^5 - \cos x}{\sin x}\]
If |x| < 1 and y = 1 + x + x2 + x3 + ..., then write the value of \[\frac{dy}{dx}\]
If f (x) = \[\log_{x_2}\]write the value of f' (x).
Find the derivative of f(x) = tan(ax + b), by first principle.
