Advertisements
Advertisements
प्रश्न
If f (x) = \[\log_{x_2}\]write the value of f' (x).
उत्तर
\[f(x) = \log_{x^2} x^3 \]
\[ = \frac{\log x^3}{\log x^2} (\text{ Change of base property })\]
\[ = \frac{3 \log x}{2 \log x}\]
\[ = \frac{3}{2}\]
\[f'\left( x \right) = 0 (\text{ Since } \frac{3}{2} \text{ is a constant })\]
APPEARS IN
संबंधित प्रश्न
Find the derivative of x at x = 1.
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):
(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)`
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):
`cos x/(1 + sin x)`
Find the derivative of f (x) = x2 − 2 at x = 10
Find the derivative of the following function at the indicated point:
k xn
Differentiate of the following from first principle:
\[\cos\left( x - \frac{\pi}{8} \right)\]
Differentiate of the following from first principle:
sin (2x − 3)
Differentiate each of the following from first principle:
\[\sqrt{\sin 2x}\]
Differentiate each of the following from first principle:
x2 sin x
Differentiate each of the following from first principle:
\[\sqrt{\sin (3x + 1)}\]
Differentiate each of the following from first principle:
\[e^\sqrt{2x}\]
Differentiate each of the following from first principle:
\[3^{x^2}\]
\[\sqrt{\tan x}\]
3x + x3 + 33
ex log a + ea long x + ea log a
Find the slope of the tangent to the curve f (x) = 2x6 + x4 − 1 at x = 1.
\[If y = \sqrt{\frac{x}{a}} + \sqrt{\frac{a}{x}}, \text{ prove that } 2xy\frac{dy}{dx} = \left( \frac{x}{a} - \frac{a}{x} \right)\]
xn tan x
(x3 + x2 + 1) sin x
sin x cos x
x5 ex + x6 log x
(1 − 2 tan x) (5 + 4 sin x)
\[\frac{x^2 \cos\frac{\pi}{4}}{\sin x}\]
x5 (3 − 6x−9)
x−4 (3 − 4x−5)
\[\frac{2x - 1}{x^2 + 1}\]
\[\frac{e^x}{1 + x^2}\]
\[\frac{x \tan x}{\sec x + \tan x}\]
\[\frac{x \sin x}{1 + \cos x}\]
\[\frac{x + \cos x}{\tan x}\]
Write the value of \[\frac{d}{dx}\left( \log \left| x \right| \right)\]
Mark the correct alternative in of the following:
If \[y = \frac{1 + \frac{1}{x^2}}{1 - \frac{1}{x^2}}\] then \[\frac{dy}{dx} =\]
