Advertisements
Advertisements
प्रश्न
\[\text{ If } y = \frac{2 x^9}{3} - \frac{5}{7} x^7 + 6 x^3 - x, \text{ find } \frac{dy}{dx} at x = 1 .\]
Advertisements
उत्तर
\[\frac{dy}{dx} = \frac{d}{dx}\left( \frac{2 x^9}{3} - \frac{5}{7} x^7 + 6 x^3 - x \right)\]
\[ = \frac{2}{3}\frac{d}{dx}\left( x^9 \right) - \frac{5}{7}\frac{d}{dx}\left( x^7 \right) + 6\frac{d}{dx}\left( x^3 \right) - \frac{d}{dx}\left( x \right)\]
\[ = \frac{2}{3}\left( 9 x^8 \right) - \frac{5}{7}\left( 7 x^6 \right) + 6\left( 3 x^2 \right) - 1\]
\[ = 6 x^8 - 5 x^6 + 18 x^2 - 1\]
\[\frac{dy}{dx} at x = 1:\]
\[6 \left( 1 \right)^8 - 5 \left( 1 \right)^6 + 18 \left( 1 \right)^2 - 1\]
\[ = 6 - 5 + 18 - 1\]
\[ = 18\]
APPEARS IN
संबंधित प्रश्न
Find the derivative of x at 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):
`1/(ax^2 + bx + c)`
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 f (x) = cos x at x = 0
Find the derivative of f (x) = tan x at x = 0
\[\frac{x^2 - 1}{x}\]
\[\frac{x + 1}{x + 2}\]
\[\frac{1}{\sqrt{3 - x}}\]
(x + 2)3
Differentiate of the following from first principle:
x cos x
Differentiate each of the following from first principle:
\[\frac{\cos x}{x}\]
Differentiate each of the following from first principle:
\[\sqrt{\sin (3x + 1)}\]
\[\cos \sqrt{x}\]
x4 − 2 sin x + 3 cos x
\[\frac{x^3}{3} - 2\sqrt{x} + \frac{5}{x^2}\]
\[If y = \sqrt{\frac{x}{a}} + \sqrt{\frac{a}{x}}, \text{ prove that } 2xy\frac{dy}{dx} = \left( \frac{x}{a} - \frac{a}{x} \right)\]
For the function \[f(x) = \frac{x^{100}}{100} + \frac{x^{99}}{99} + . . . + \frac{x^2}{2} + x + 1 .\]
sin x cos x
(x sin x + cos x ) (ex + x2 log 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
(ax + b)n (cx + d)n
\[\frac{2x - 1}{x^2 + 1}\]
\[\frac{x + e^x}{1 + \log x}\]
\[\frac{e^x}{1 + x^2}\]
\[\frac{x \sin x}{1 + \cos x}\]
\[\frac{\sin x - x \cos x}{x \sin x + \cos x}\]
\[\frac{a + \sin x}{1 + a \sin x}\]
\[\frac{3^x}{x + \tan x}\]
\[\frac{\sec x - 1}{\sec x + 1}\]
\[\frac{ax + b}{p x^2 + qx + r}\]
\[\frac{1}{a x^2 + bx + c}\]
Write the value of \[\frac{d}{dx}\left( x \left| x \right| \right)\]
Write the value of \[\frac{d}{dx} \left\{ \left( x + \left| x \right| \right) \left| x \right| \right\}\]
If f (x) = \[\frac{x^2}{\left| x \right|},\text{ write }\frac{d}{dx}\left( f (x) \right)\]
Find the derivative of x2 cosx.
Find the derivative of f(x) = tan(ax + b), by first principle.
(ax2 + cot x)(p + q cos x)
