Advertisements
Advertisements
प्रश्न
\[\frac{1 + 3^x}{1 - 3^x}\]
Advertisements
उत्तर
\[\text{ Let } u = 1 + 3^x ; v = 1 - 3^x \]
\[\text{ Then }, u' = 3^x \log 3; v' = - 3^x \log 3\]
\[\text{ Using the quotient rule }:\]
\[\frac{d}{dx}\left( \frac{u}{v} \right) = \frac{vu' - uv'}{v^2}\]
\[\frac{d}{dx}\left( \frac{1 + 3^x}{1 - 3^x} \right) = \frac{\left( 1 - 3^x \right) 3^x \log 3 - \left( 1 + 3^x \right)\left( - 3^x \log 3 \right)}{\left( 1 - 3^x \right)^2}\]
\[ = \frac{3^x \log 3 - 3^{2x} \log 3 + 3^x \log 3 + 3^{2x} \log 3}{\left( 1 - 3^x \right)^2}\]
\[ = \frac{2 . 3^x \log 3}{\left( 1 - 3^x \right)^2}\]
APPEARS IN
संबंधित प्रश्न
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):
`(px+ q) (r/s + s)`
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^2 +qx + r)/(ax +b)`
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 f (x) = x2 − 2 at x = 10
\[\frac{x + 2}{3x + 5}\]
k xn
(x + 2)3
\[\sqrt{2 x^2 + 1}\]
\[\frac{2x + 3}{x - 2}\]
Differentiate each of the following from first principle:
\[\sqrt{\sin (3x + 1)}\]
Differentiate each of the following from first principle:
\[e^{x^2 + 1}\]
Differentiate each of the following from first principle:
\[e^\sqrt{ax + b}\]
\[\cos \sqrt{x}\]
(2x2 + 1) (3x + 2)
2 sec x + 3 cot x − 4 tan x
\[\frac{(x + 5)(2 x^2 - 1)}{x}\]
Find the slope of the tangent to the curve f (x) = 2x6 + x4 − 1 at x = 1.
For the function \[f(x) = \frac{x^{100}}{100} + \frac{x^{99}}{99} + . . . + \frac{x^2}{2} + x + 1 .\]
x2 ex log x
(x sin x + cos x) (x cos x − sin x)
(1 − 2 tan x) (5 + 4 sin x)
sin2 x
logx2 x
x5 (3 − 6x−9)
Differentiate in two ways, using product rule and otherwise, the function (1 + 2 tan x) (5 + 4 cos x). Verify that the answers are the same.
\[\frac{x^2 + 1}{x + 1}\]
\[\frac{e^x - \tan x}{\cot x - x^n}\]
\[\frac{x}{1 + \tan x}\]
\[\frac{\sec x - 1}{\sec x + 1}\]
Write the value of \[\lim_{x \to c} \frac{f(x) - f(c)}{x - c}\]
Write the value of \[\frac{d}{dx} \left\{ \left( x + \left| x \right| \right) \left| x \right| \right\}\]
Write the value of the derivative of f (x) = |x − 1| + |x − 3| at x = 2.
If f (x) = |x| + |x−1|, write the value of \[\frac{d}{dx}\left( f (x) \right)\]
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\[f\left( x \right) = 1 - x + x^2 - x^3 + . . . - x^{99} + x^{100}\]then \[f'\left( 1 \right)\]
Mark the correct alternative in of the following:
If f(x) = x sinx, then \[f'\left( \frac{\pi}{2} \right) =\]
Find the derivative of 2x4 + x.
