Advertisements
Advertisements
Question
If f (x) = \[\log_{x_2}\]write the value of f' (x).
Advertisements
Solution
\[f(x) = \log_{x^2} x^3 \]
\[ = \frac{\log x^3}{\log x^2} (\text{ Change of base property })\]
\[ = \frac{3 \log x}{2 \log x}\]
\[ = \frac{3}{2}\]
\[f'\left( x \right) = 0 (\text{ Since } \frac{3}{2} \text{ is a constant })\]
APPEARS IN
RELATED QUESTIONS
Find the derivative of x–4 (3 – 4x–5).
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 (cx + d)m
Find the derivative of f (x) = tan x at x = 0
Find the derivative of the following function at the indicated point:
sin 2x at x =\[\frac{\pi}{2}\]
\[\frac{1}{\sqrt{x}}\]
\[\frac{x + 1}{x + 2}\]
\[\frac{1}{\sqrt{3 - x}}\]
(x2 + 1) (x − 5)
\[\sqrt{2 x^2 + 1}\]
\[\frac{2x + 3}{x - 2}\]
Differentiate of the following from first principle:
e3x
Differentiate of the following from first principle:
− x
Differentiate each of the following from first principle:
\[3^{x^2}\]
tan2 x
\[\sin \sqrt{2x}\]
(2x2 + 1) (3x + 2)
\[\left( x + \frac{1}{x} \right)\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)\]
a0 xn + a1 xn−1 + a2 xn−2 + ... + an−1 x + an.
\[\log\left( \frac{1}{\sqrt{x}} \right) + 5 x^a - 3 a^x + \sqrt[3]{x^2} + 6 \sqrt[4]{x^{- 3}}\]
\[\text{ If } y = \frac{2 x^9}{3} - \frac{5}{7} x^7 + 6 x^3 - x, \text{ find } \frac{dy}{dx} at x = 1 .\]
If for f (x) = λ x2 + μ x + 12, f' (4) = 15 and f' (2) = 11, then find λ and μ.
(x3 + x2 + 1) sin x
sin x cos x
x5 ex + x6 log x
(1 − 2 tan x) (5 + 4 sin x)
\[\frac{x^2 + 1}{x + 1}\]
\[\frac{e^x - \tan x}{\cot x - x^n}\]
\[\frac{x}{1 + \tan x}\]
\[\frac{e^x}{1 + x^2}\]
\[\frac{x \sin x}{1 + \cos x}\]
\[\frac{4x + 5 \sin x}{3x + 7 \cos x}\]
If x < 2, then write the value of \[\frac{d}{dx}(\sqrt{x^2 - 4x + 4)}\]
Write the value of the derivative of f (x) = |x − 1| + |x − 3| at x = 2.
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 \[y = \sqrt{x} + \frac{1}{\sqrt{x}}\] then \[\frac{dy}{dx}\] at x = 1 is
Mark the correct alternative in of the following:
If \[f\left( x \right) = x^{100} + x^{99} + . . . + x + 1\] then \[f'\left( 1 \right)\] is equal to
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
`(a + b sin x)/(c + d cos x)`
Let f(x) = x – [x]; ∈ R, then f'`(1/2)` is ______.
