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):
`(a + bsin x)/(c + dcosx)`
Advertisements
उत्तर
Let f(x) = `(a + b sinx)/(c + d cosx)`
∴ `f'(x) = ([d/dx (a + b sinx)](c + d cos x)- (a + b sin x)d/dx(c + d cosx))/(c + dcosx)^2`
= `(b cosx(c + dcosx) - (a + b sinx)(-d sin x))/(c + d cosx)^2`
= `(bc cosx + bd cos^2 x +ad sinx + bd sin^2 x)/(c + dcosx)^2`
= `(bc cosx + ad sinx + bd(sin^2x + cos^2 x))/(c + dcosx)^2`
= `(bd cosx + ad sinx + bd)/(c + dcosx)^2`
APPEARS IN
संबंधित प्रश्न
Find the derivative of (5x3 + 3x – 1) (x – 1).
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):
`(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):
`(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):
`(sin x + cos x)/(sin x - 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):
`(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):
sinn x
Find the derivative of f (x) = 99x at x = 100
Find the derivative of f (x) x at x = 1
Find the derivative of f (x) = cos x at x = 0
(x + 2)3
Differentiate each of the following from first principle:
e−x
Differentiate of the following from first principle:
eax + b
Differentiate of the following from first principle:
sin (2x − 3)
Differentiate each of the following from first principle:
\[3^{x^2}\]
tan (2x + 1)
log3 x + 3 loge x + 2 tan x
\[\frac{2 x^2 + 3x + 4}{x}\]
Find the slope of the tangent to the curve f (x) = 2x6 + x4 − 1 at x = 1.
For the function \[f(x) = \frac{x^{100}}{100} + \frac{x^{99}}{99} + . . . + \frac{x^2}{2} + x + 1 .\]
\[\frac{2^x \cot x}{\sqrt{x}}\]
(x sin x + cos x) (x cos x − sin x)
(1 +x2) cos x
(ax + b) (a + d)2
\[\frac{2x - 1}{x^2 + 1}\]
\[\frac{e^x - \tan x}{\cot x - x^n}\]
\[\frac{a x^2 + bx + c}{p x^2 + qx + r}\]
\[\frac{x^2 - x + 1}{x^2 + x + 1}\]
\[\frac{\sqrt{a} + \sqrt{x}}{\sqrt{a} - \sqrt{x}}\]
\[\frac{a + b \sin x}{c + d \cos x}\]
\[\frac{x + \cos x}{\tan x}\]
\[\frac{1}{a x^2 + bx + c}\]
Write the value of \[\lim_{x \to c} \frac{f(x) - f(c)}{x - c}\]
If x < 2, then write the value of \[\frac{d}{dx}(\sqrt{x^2 - 4x + 4)}\]
Write the value of \[\frac{d}{dx} \left\{ \left( x + \left| x \right| \right) \left| x \right| \right\}\]
Write the value of the derivative of f (x) = |x − 1| + |x − 3| at x = 2.
If f (x) = \[\frac{x^2}{\left| x \right|},\text{ write }\frac{d}{dx}\left( f (x) \right)\]
(ax2 + cot x)(p + q cos x)
