Advertisements
Advertisements
प्रश्न
logx2 x
Advertisements
उत्तर
\[\log_{x^2} x = \frac{\log x}{\log x^2} (\text{ by change of base property })\]
\[ = \frac{\log x}{2 \log x} \left[ \log x^2 = 2 \log x \right]\]
\[ = \frac{1}{2}\]
\[\text{ Now }\frac{d}{dx}\left( \log_{x^2} x \right)=\frac{d}{dx}\left( \frac{1}{2} \right)\]
\[ = 0 \left( \because\frac{1}{2}\text{ is a constant } \right )\]
APPEARS IN
संबंधित प्रश्न
Find the derivative of x5 (3 – 6x–9).
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)`
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 + 1/x)/(1- 1/x)`
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/x^4 = b/x^2 + cos x`
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):
`(sin x + cos x)/(sin x - cos x)`
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 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):
x4 (5 sin x – 3 cos x)
Find the derivative of f (x) x at x = 1
Find the derivative of the following function at the indicated point:
2 cos x at x =\[\frac{\pi}{2}\]
Find the derivative of the following function at the indicated point:
sin 2x at x =\[\frac{\pi}{2}\]
\[\frac{x^2 - 1}{x}\]
(x2 + 1) (x − 5)
Differentiate of the following from first principle:
x sin x
\[\sqrt{\tan x}\]
\[\sin \sqrt{2x}\]
\[\tan \sqrt{x}\]
x4 − 2 sin x + 3 cos x
3x + x3 + 33
\[\frac{x^3}{3} - 2\sqrt{x} + \frac{5}{x^2}\]
log3 x + 3 loge x + 2 tan x
x3 sin x
xn tan x
(x3 + x2 + 1) sin x
(x sin x + cos x) (x cos x − sin x)
\[e^x \log \sqrt{x} \tan x\]
x−4 (3 − 4x−5)
x−3 (5 + 3x)
\[\frac{x + e^x}{1 + \log x}\]
\[\frac{1}{a x^2 + bx + c}\]
\[\frac{x}{1 + \tan x}\]
\[\frac{x + \cos x}{\tan x}\]
Write the derivative of f (x) = 3 |2 + x| at x = −3.
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
(ax2 + cot x)(p + q cos x)
