Advertisements
Advertisements
प्रश्न
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)`
Advertisements
उत्तर
Let f(x) = `(sec x - 1)/(sec x + 1)`
f(x) = `(1/cos x -1)/(1/cos x +1)`
= `(1 - cos x)/(1 + cos x)`
By quotient rule,
f'(x) = `((1 + cosx)d/dx(1 - cosx)-(1 - cos x)d/dx(1 + cos x))/((1 + cos x^2))`
= `((1 + cos x) (sin x) - (1 - cos x) (-sin x))/((1 + cos x)^2)`
= `(sin x + cos x sin x + sin x - sin x cos x) /(1 + cos x)^2`
= `(2 sin x)/(1 + cos x)^2`
= `(2 sin x)/(1 + 1/sec x)^2 = (2 sin x)/((sec x + 1)^2/(sec^2 x))`
= `(2 sin x sec^2x)/ (secx+1)^2`
= `((2 sin x)/(cos x)sec x)/(sec x + 1)^2`
= `(2sec x tan x)/(sec x + 1)^2`
APPEARS IN
संबंधित प्रश्न
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)2
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/x^4 = b/x^2 + cos x`
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):
cosec x cot x
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)`
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):
x4 (5 sin x – 3 cos x)
Find the derivative of f (x) = cos x at x = 0
Find the derivative of the following function at the indicated point:
Find the derivative of the following function at the indicated point:
2 cos x at x =\[\frac{\pi}{2}\]
\[\frac{1}{\sqrt{x}}\]
\[\frac{x^2 + 1}{x}\]
\[\frac{x + 1}{x + 2}\]
k xn
\[\frac{1}{\sqrt{3 - x}}\]
(x + 2)3
Differentiate of the following from first principle:
e3x
Differentiate of the following from first principle:
− x
Differentiate of the following from first principle:
\[\cos\left( x - \frac{\pi}{8} \right)\]
Differentiate each of the following from first principle:
\[\frac{\sin x}{x}\]
tan (2x + 1)
\[\tan \sqrt{x}\]
\[\left( x + \frac{1}{x} \right)\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)\]
a0 xn + a1 xn−1 + a2 xn−2 + ... + an−1 x + an.
\[\frac{1}{\sin x} + 2^{x + 3} + \frac{4}{\log_x 3}\]
(1 +x2) cos x
x3 ex cos x
(2x2 − 3) sin x
\[\frac{2x - 1}{x^2 + 1}\]
\[\frac{e^x - \tan x}{\cot x - x^n}\]
\[\frac{1}{a x^2 + bx + c}\]
\[\frac{2^x \cot x}{\sqrt{x}}\]
\[\frac{\sin x - x \cos x}{x \sin x + \cos x}\]
\[\frac{3^x}{x + \tan x}\]
\[\frac{x + \cos x}{\tan x}\]
If x < 2, then write the value of \[\frac{d}{dx}(\sqrt{x^2 - 4x + 4)}\]
Write the value of \[\frac{d}{dx} \left\{ \left( x + \left| x \right| \right) \left| x \right| \right\}\]
If f (x) = \[\frac{x^2}{\left| x \right|},\text{ write }\frac{d}{dx}\left( f (x) \right)\]
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\[f\left( x \right) = 1 + x + \frac{x^2}{2} + . . . + \frac{x^{100}}{100}\] then \[f'\left( 1 \right)\] is equal to
Find the derivative of f(x) = tan(ax + b), by first principle.
`(a + b sin x)/(c + d cos x)`
