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 `2x - 3/4`
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):
`(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):
`(a + bsin x)/(c + dcosx)`
Find the derivative of f (x) = cos x at x = 0
Find the derivative of the following function at the indicated point:
sin 2x at x =\[\frac{\pi}{2}\]
\[\frac{1}{x^3}\]
\[\frac{1}{\sqrt{3 - x}}\]
x2 + x + 3
Differentiate of the following from first principle:
− x
Differentiate of the following from first principle:
\[\cos\left( x - \frac{\pi}{8} \right)\]
Differentiate of the following from first principle:
x sin x
Differentiate each of the following from first principle:
sin x + cos x
\[\tan \sqrt{x}\]
\[\tan \sqrt{x}\]
a0 xn + a1 xn−1 + a2 xn−2 + ... + an−1 x + an.
\[If y = \sqrt{\frac{x}{a}} + \sqrt{\frac{a}{x}}, \text{ prove that } 2xy\frac{dy}{dx} = \left( \frac{x}{a} - \frac{a}{x} \right)\]
(x sin x + cos x ) (ex + x2 log 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.
(x + 2) (x + 3)
(ax + b) (a + d)2
(ax + b)n (cx + d)n
\[\frac{e^x + \sin x}{1 + \log x}\]
\[\frac{\sin x - x \cos x}{x \sin x + \cos x}\]
\[\frac{\sqrt{a} + \sqrt{x}}{\sqrt{a} - \sqrt{x}}\]
\[\frac{a + b \sin x}{c + d \cos x}\]
\[\frac{x^5 - \cos x}{\sin x}\]
\[\frac{x}{\sin^n x}\]
Write the value of \[\lim_{x \to c} \frac{f(x) - f(c)}{x - c}\]
If x < 2, then write the value of \[\frac{d}{dx}(\sqrt{x^2 - 4x + 4)}\]
If f (1) = 1, f' (1) = 2, then write the value of \[\lim_{x \to 1} \frac{\sqrt{f (x)} - 1}{\sqrt{x} - 1}\]
Mark the correct alternative in of the following:
Let f(x) = x − [x], x ∈ R, then \[f'\left( \frac{1}{2} \right)\]
Find the derivative of f(x) = tan(ax + b), by first principle.
Let f(x) = x – [x]; ∈ R, then f'`(1/2)` is ______.
