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):
`cos x/(1 + sin x)`
Advertisements
उत्तर
Let f(x) = `(cos x)/(1 + sin x)`
By quotient rule,
f'(x) = `((1 + sin x)d/dx(cos x) - (cos x)d/dx (1 + sin x))/(1 + sin x)^2`
= `((1 + sin x) (-sin x) - (cos x) (cos x))/(1 + sin x)^2`
= `(-sin x - sin^2 x - cos^2 x)/(1 + sin x)^2`
= `(-sin x - (sin^2 x - cos^2 x))/(1 + sin x)^2`
= `(-sin x - 1)/(1 + sin x)^2`
= `(-(1 + sin x))/(1 + sin x)^2`
= `(-1 )/((1 + sin x))`
APPEARS IN
संबंधित प्रश्न
Find the derivative of x at x = 1.
Find the derivative of x–4 (3 – 4x–5).
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 f (x) = x2 − 2 at x = 10
Find the derivative of f (x) x at x = 1
\[\frac{1}{\sqrt{x}}\]
(x2 + 1) (x − 5)
Differentiate each of the following from first principle:
e−x
Differentiate of the following from first principle:
sin (x + 1)
Differentiate each of the following from first principle:
\[\sqrt{\sin 2x}\]
Differentiate each of the following from first principle:
x2 sin x
Differentiate each of the following from first principle:
\[e^{x^2 + 1}\]
x4 − 2 sin x + 3 cos x
\[\frac{x^3}{3} - 2\sqrt{x} + \frac{5}{x^2}\]
\[\left( x + \frac{1}{x} \right)\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)\]
\[\frac{2 x^2 + 3x + 4}{x}\]
\[\frac{( x^3 + 1)(x - 2)}{x^2}\]
\[\frac{a \cos x + b \sin x + c}{\sin x}\]
2 sec x + 3 cot x − 4 tan x
\[\frac{(x + 5)(2 x^2 - 1)}{x}\]
xn tan x
sin x cos x
x5 (3 − 6x−9)
x−4 (3 − 4x−5)
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)
\[\frac{x^2 + 1}{x + 1}\]
\[\frac{a x^2 + bx + c}{p x^2 + qx + r}\]
\[\frac{e^x}{1 + x^2}\]
\[\frac{x \sin x}{1 + \cos x}\]
\[\frac{1 + 3^x}{1 - 3^x}\]
\[\frac{x}{\sin^n x}\]
\[\frac{ax + b}{p x^2 + qx + r}\]
If f (x) = \[\frac{x^2}{\left| x \right|},\text{ write }\frac{d}{dx}\left( f (x) \right)\]
If f (x) = |x| + |x−1|, write the value of \[\frac{d}{dx}\left( f (x) \right)\]
Write the value of \[\frac{d}{dx}\left( \log \left| x \right| \right)\]
Mark the correct alternative in of the following:
If \[f\left( x \right) = \frac{x - 4}{2\sqrt{x}}\]
Find the derivative of 2x4 + x.
