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):
`(sin x + cos x)/(sin x - cos x)`
उत्तर
Let f(x) = `(sinx + cosx)/(sinx - cosx)`
∴ `f'(x) = ([d/dx(sin x + cos x)] (sin x - cos x) - (sin x +cos x) d/dx (sin x - cos x))/(sin x - cos x)^2`
= `((cos x - sin x)(sin x - cos x) - (sin x + cos x)(cos x + sin x))/(sin x - cos x)^2`
= `(-(cos x - sin x)^2 - (sin x + cos x)^2)/(sin x - cos x)^2`
= `(-(cos^2 x + sin^2 x - 2 cosx sinx) - (cos^2 x + sin^2 x + 2 sin x cos x))/(sin x - cosx)^2`
= `(1 - 2sin xcos x + 1 + 2 cosx sin x)/(sin x - cosx)^2`
= `(-2)/(sin x - cosx)^2`
APPEARS IN
संबंधित प्रश्न
Find the derivative of x2 – 2 at x = 10.
Find the derivative of x–3 (5 + 3x).
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):
(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)
Find the derivative of f (x) = 3x at x = 2
Find the derivative of f (x) = tan x at x = 0
\[\frac{x^2 + 1}{x}\]
(x2 + 1) (x − 5)
Differentiate of the following from first principle:
x sin x
Differentiate each of the following from first principle:
x2 sin x
Differentiate each of the following from first principle:
\[\sqrt{\sin (3x + 1)}\]
Differentiate each of the following from first principle:
sin x + cos x
Differentiate each of the following from first principle:
\[a^\sqrt{x}\]
tan2 x
tan 2x
\[\cos \sqrt{x}\]
log3 x + 3 loge x + 2 tan x
\[\text{ If } y = \left( \sin\frac{x}{2} + \cos\frac{x}{2} \right)^2 , \text{ find } \frac{dy}{dx} at x = \frac{\pi}{6} .\]
x3 sin x
x2 ex log x
\[e^x \log \sqrt{x} \tan x\]
\[\frac{x^2 \cos\frac{\pi}{4}}{\sin x}\]
Differentiate each of the following functions by the product rule and the other method and verify that answer from both the methods is the same.
(x + 2) (x + 3)
(ax + b) (a + d)2
\[\frac{a x^2 + bx + c}{p x^2 + qx + r}\]
\[\frac{x \sin x}{1 + \cos x}\]
\[\frac{x^5 - \cos x}{\sin x}\]
\[\frac{x + \cos x}{\tan x}\]
\[\frac{ax + b}{p x^2 + qx + r}\]
If f (x) = \[\frac{x^2}{\left| x \right|},\text{ write }\frac{d}{dx}\left( f (x) \right)\]
Write the value of \[\frac{d}{dx}\left( \log \left| x \right| \right)\]
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 \[y = \frac{\sin\left( x + 9 \right)}{\cos x}\] then \[\frac{dy}{dx}\] at x = 0 is
Mark the correct alternative in each of the following:
If\[f\left( x \right) = \frac{x^n - a^n}{x - a}\] then \[f'\left( a \right)\]
Find the derivative of x2 cosx.
(ax2 + cot x)(p + q cos x)
