Advertisements
Advertisements
Question
\[\frac{{10}^x}{\sin x}\]
Advertisements
Solution
\[\text{ Let } u = {10}^x ; v = \sin x\]
\[\text{ Then }, u' = {10}^x \log 10; v' = \cos x\]
\[\text{ Using the quotient rule }:\]
\[\frac{d}{dx}\left( \frac{u}{v} \right) = \frac{vu' - uv'}{v^2}\]
\[\frac{d}{dx}\left( \frac{{10}^x}{\sin x} \right) = \frac{\sin x {10}^x \log 10 - {10}^x \cos x}{\sin^2 x}\]
\[ = \frac{\sin x {10}^x \log 10}{\sin^2 x} - \frac{{10}^x \cos x}{\sin^2 x}\]
\[ = {10}^x \log 10 \cos ec x - {10}^x cosec x \cot x\]
\[ = {10}^x cosec x\left( \log 10 - \cot x \right)\]
APPEARS IN
RELATED QUESTIONS
Find the derivative of 99x at x = 100.
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):
(ax + b)n (cx + d)m
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 + a))/ cos x`
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 =\[\frac{\pi}{2}\]
\[\frac{x^2 + 1}{x}\]
k xn
\[\frac{1}{\sqrt{3 - x}}\]
(x + 2)3
(x2 + 1) (x − 5)
Differentiate each of the following from first principle:
e−x
Differentiate of the following from first principle:
(−x)−1
Differentiate of the following from first principle:
\[\cos\left( x - \frac{\pi}{8} \right)\]
Differentiate each of the following from first principle:
\[\sqrt{\sin 2x}\]
Differentiate each of the following from first principle:
\[\frac{\sin x}{x}\]
Differentiate each of the following from first principle:
\[\frac{\cos x}{x}\]
Differentiate each of the following from first principle:
x2 sin x
\[\sqrt{\tan x}\]
3x + x3 + 33
\[\frac{( x^3 + 1)(x - 2)}{x^2}\]
a0 xn + a1 xn−1 + a2 xn−2 + ... + an−1 x + an.
xn loga x
(x sin x + cos x) (x cos x − sin x)
(x sin x + cos x ) (ex + x2 log x)
(1 − 2 tan x) (5 + 4 sin x)
x4 (5 sin x − 3 cos x)
x−4 (3 − 4x−5)
(ax + b) (a + d)2
\[\frac{e^x - \tan x}{\cot x - x^n}\]
\[\frac{a x^2 + bx + c}{p x^2 + qx + r}\]
\[\frac{x}{1 + \tan x}\]
\[\frac{e^x}{1 + x^2}\]
\[\frac{p x^2 + qx + r}{ax + b}\]
Write the value of \[\lim_{x \to c} \frac{f(x) - f(c)}{x - c}\]
If f (x) = \[\frac{x^2}{\left| x \right|},\text{ write }\frac{d}{dx}\left( f (x) \right)\]
Write the derivative of f (x) = 3 |2 + x| at x = −3.
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
`(a + b sin x)/(c + d cos x)`
