Advertisements
Advertisements
प्रश्न
xn loga x
Advertisements
उत्तर
\[\text{ Let } u = x^n ; v = \log_a x = \frac{\log x}{\log a}\]
\[\text{ Then }, u' = n x^{n - 1} ; v' = \frac{1}{x \log a}\]
\[\text{ Using the product rule }:\]
\[\frac{d}{dx}\left( uv \right) = uv' + vu'\]
\[\frac{d}{dx}\left( x^n \log_a x \right) = x^n . \frac{1}{x \log a} + \log_a x \left( n x^{n - 1} \right)\]
\[ = x^{n - 1} \frac{1}{\log a} + \log_a x \left( n x^{n - 1} \right)\]
\[ = x^{n - 1} \left( \frac{1}{\log a} + n \log_a x \right)\]
APPEARS IN
संबंधित प्रश्न
Find the derivative of x2 – 2 at x = 10.
Find the derivative of `2x - 3/4`
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):
`(px+ q) (r/s + s)`
Find the derivative of f (x) = x2 − 2 at x = 10
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 =\[\frac{\pi}{2}\]
\[\frac{x + 1}{x + 2}\]
k xn
(x + 2)3
(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:
x2 sin x
Differentiate each of the following from first principle:
\[a^\sqrt{x}\]
\[\frac{2 x^2 + 3x + 4}{x}\]
\[\frac{a \cos x + b \sin x + c}{\sin x}\]
2 sec x + 3 cot x − 4 tan x
(x3 + x2 + 1) sin x
x5 ex + x6 log x
sin2 x
\[\frac{x^2 \cos\frac{\pi}{4}}{\sin x}\]
x−3 (5 + 3x)
(ax + b)n (cx + d)n
\[\frac{1 + \log x}{1 - \log x}\]
\[\frac{p x^2 + qx + r}{ax + b}\]
\[\frac{x^5 - \cos x}{\sin x}\]
\[\frac{x}{\sin^n x}\]
If \[\frac{\pi}{2}\] then find \[\frac{d}{dx}\left( \sqrt{\frac{1 + \cos 2x}{2}} \right)\]
If f (x) = \[\frac{x^2}{\left| x \right|},\text{ write }\frac{d}{dx}\left( f (x) \right)\]
If f (x) = |x| + |x−1|, write the value of \[\frac{d}{dx}\left( f (x) \right)\]
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
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
Find the derivative of f(x) = tan(ax + b), by first principle.
