Advertisements
Advertisements
प्रश्न
\[\log\left( \frac{1}{\sqrt{x}} \right) + 5 x^a - 3 a^x + \sqrt[3]{x^2} + 6 \sqrt[4]{x^{- 3}}\]
Advertisements
उत्तर
\[ = \frac{d}{dx}\left[ log \left( x^\frac{- 1}{2} \right) \right] + 5\frac{d}{dx}\left( x^a \right) - 3\frac{d}{dx}\left( a^x \right) + \frac{d}{dx}\left( x^\frac{2}{3} \right) + 6\frac{d}{dx}\left( x^\frac{- 3}{4} \right)\]
\[ = \frac{d}{dx}\left( \frac{- 1}{2}\log x \right) + 5\frac{d}{dx}\left( x^a \right) - 3\frac{d}{dx}\left( a^x \right) + \frac{d}{dx}\left( x^\frac{2}{3} \right) + 6\frac{d}{dx}\left( x^\frac{- 3}{4} \right)\]
\[ = \frac{- 1}{2} . \frac{1}{x} + 5a x^{a - 1} - 3 a^x \log a + \frac{2}{3} x^\frac{- 1}{3} + 6\left( \frac{- 3}{4} \right) x^\frac{- 7}{4} \]
\[ = \frac{- 1}{2x} + 5a x^{a - 1} - 3 a^x \log a + \frac{2}{3} x^\frac{- 1}{3} - \frac{9}{2} x^\frac{- 7}{4} \]
\[\]
APPEARS IN
संबंधित प्रश्न
Find the derivative of x2 – 2 at x = 10.
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
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):
sinn x
Find the derivative of f (x) = x2 − 2 at x = 10
Find the derivative of f (x) = tan x at x = 0
Find the derivative of the following function at the indicated point:
sin x at x =\[\frac{\pi}{2}\]
Find the derivative of the following function at the indicated point:
\[\frac{2}{x}\]
\[\frac{x + 1}{x + 2}\]
(x2 + 1) (x − 5)
(x2 + 1) (x − 5)
Differentiate of the following from first principle:
(−x)−1
Differentiate each of the following from first principle:
\[\sqrt{\sin 2x}\]
Differentiate each of the following from first principle:
\[3^{x^2}\]
\[\tan \sqrt{x}\]
3x + x3 + 33
\[\frac{a \cos x + b \sin x + c}{\sin x}\]
\[\frac{1}{\sin x} + 2^{x + 3} + \frac{4}{\log_x 3}\]
\[\text{ If } y = \left( \frac{2 - 3 \cos x}{\sin x} \right), \text{ find } \frac{dy}{dx} at x = \frac{\pi}{4}\]
Find the slope of the tangent to the curve f (x) = 2x6 + x4 − 1 at x = 1.
\[If y = \sqrt{\frac{x}{a}} + \sqrt{\frac{a}{x}}, \text{ prove that } 2xy\frac{dy}{dx} = \left( \frac{x}{a} - \frac{a}{x} \right)\]
\[\text{ If } y = \frac{2 x^9}{3} - \frac{5}{7} x^7 + 6 x^3 - x, \text{ find } \frac{dy}{dx} at x = 1 .\]
xn tan x
(x3 + x2 + 1) sin x
sin x cos x
(1 − 2 tan x) (5 + 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.
(3 sec x − 4 cosec x) (−2 sin x + 5 cos x)
(ax + b) (a + d)2
\[\frac{a x^2 + bx + c}{p x^2 + qx + r}\]
\[\frac{x \sin x}{1 + \cos x}\]
\[\frac{\sin x - x \cos x}{x \sin x + \cos x}\]
\[\frac{\sqrt{a} + \sqrt{x}}{\sqrt{a} - \sqrt{x}}\]
\[\frac{x}{1 + \tan x}\]
\[\frac{p x^2 + qx + r}{ax + b}\]
Write the value of \[\lim_{x \to c} \frac{f(x) - f(c)}{x - c}\]
If \[\frac{\pi}{2}\] then find \[\frac{d}{dx}\left( \sqrt{\frac{1 + \cos 2x}{2}} \right)\]
Mark the correct alternative in of the following:
If\[f\left( x \right) = 1 - x + x^2 - x^3 + . . . - x^{99} + x^{100}\]then \[f'\left( 1 \right)\]
Mark the correct alternative in of the following:
If \[y = \frac{\sin\left( x + 9 \right)}{\cos x}\] then \[\frac{dy}{dx}\] at x = 0 is
Mark the correct alternative in each of the following:
If\[f\left( x \right) = \frac{x^n - a^n}{x - a}\] then \[f'\left( a \right)\]
