Advertisements
Advertisements
Question
\[\frac{1}{\sin x} + 2^{x + 3} + \frac{4}{\log_x 3}\]
Advertisements
Solution
\[\frac{d}{dx}\left( \frac{1}{\sin x} + 2^{x + 3} + \frac{4}{\log_x 3} \right)\]
\[ = \frac{d}{dx}\left( \cos ec x + 2^x . 2^3 + \frac{4}{\frac{\log 3}{\log x}} \right)\]
\[ = \frac{d}{dx}\left( \cos ec x \right) + 2^3 \frac{d}{dx}\left( 2^x \right) + \frac{4}{\log 3}\frac{d}{dx}\left( \log x \right)\]
\[ = - \cos ec x cot x + 2^3 . 2^x . \log 2 + \frac{4}{\log 3} . \frac{1}{x}\]
\[ = - \cos ec x cot x + 2^{x + 3} . \log 2 + \frac{4}{x\log 3}\]
APPEARS IN
RELATED QUESTIONS
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):
`(sec x - 1)/(sec x + 1)`
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)`
\[\frac{1}{x^3}\]
\[\frac{x^2 - 1}{x}\]
\[\frac{x + 2}{3x + 5}\]
x2 + x + 3
Differentiate of the following from first principle:
− x
Differentiate of the following from first principle:
x cos x
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:
\[\frac{\sin x}{x}\]
Differentiate each of the following from first principle:
\[\frac{\cos x}{x}\]
Differentiate each of the following from first principle:
\[e^\sqrt{2x}\]
x4 − 2 sin x + 3 cos x
log3 x + 3 loge x + 2 tan x
\[\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)^3\]
a0 xn + a1 xn−1 + a2 xn−2 + ... + an−1 x + an.
\[\frac{(x + 5)(2 x^2 - 1)}{x}\]
Find the rate at which the function f (x) = x4 − 2x3 + 3x2 + x + 5 changes with respect to x.
\[\text{ If } y = \frac{2 x^9}{3} - \frac{5}{7} x^7 + 6 x^3 - x, \text{ find } \frac{dy}{dx} at x = 1 .\]
For the function \[f(x) = \frac{x^{100}}{100} + \frac{x^{99}}{99} + . . . + \frac{x^2}{2} + x + 1 .\]
x3 sin x
xn tan x
xn loga x
sin x cos x
x5 ex + x6 log x
x4 (5 sin x − 3 cos x)
\[\frac{x^2 + 1}{x + 1}\]
\[\frac{x \tan x}{\sec x + \tan x}\]
\[\frac{x \sin x}{1 + \cos x}\]
\[\frac{1 + \log x}{1 - \log x}\]
Write the value of \[\lim_{x \to c} \frac{f(x) - f(c)}{x - c}\]
Write the value of the derivative of f (x) = |x − 1| + |x − 3| at x = 2.
Write the value of \[\frac{d}{dx}\left( \log \left| x \right| \right)\]
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:
If \[f\left( x \right) = \frac{x - 4}{2\sqrt{x}}\]
Find the derivative of f(x) = tan(ax + b), by first principle.
