Advertisements
Advertisements
प्रश्न
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
पर्याय
cos 9
sin 9
0
1
Advertisements
उत्तर
\[y = \frac{\sin\left( x + 9 \right)}{\cos x}\]
Differentiating both sides with respect to x, we get
\[ = \frac{\cos x \times \cos\left( x + 9 \right) - \sin\left( x + 9 \right) \times \left( - \sin x \right)}{\cos^2 x}\]
\[ = \frac{\cos\left( x + 9 \right)\cos x + \sin\left( x + 9 \right)\sin x}{\cos^2 x}\]
\[ = \frac{\cos\left( x + 9 - x \right)}{\cos^2 x}\]
\[ = \frac{\cos9}{\cos^2 x}\]
\[\left( \frac{dy}{dx} \right)_{x = 0} = \frac{\cos9}{\cos^2 0} = \cos9\]
Thus, \[\frac{dy}{dx}\] at x = 0 is cos 9.
Hence, the correct answer is option (a).
APPEARS IN
संबंधित प्रश्न
Find the derivative of x at x = 1.
Find the derivative of `2x - 3/4`
Find the derivative of x5 (3 – 6x–9).
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) = 99x at x = 100
\[\frac{1}{x^3}\]
\[\frac{x^2 + 1}{x}\]
\[\frac{x + 2}{3x + 5}\]
k xn
Differentiate each of the following from first principle:
sin x + cos x
tan2 x
\[\sqrt{\tan x}\]
log3 x + 3 loge x + 2 tan x
\[\left( x + \frac{1}{x} \right)\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)\]
\[If y = \sqrt{\frac{x}{a}} + \sqrt{\frac{a}{x}}, \text{ prove that } 2xy\frac{dy}{dx} = \left( \frac{x}{a} - \frac{a}{x} \right)\]
\[\text{ If } y = \frac{2 x^9}{3} - \frac{5}{7} x^7 + 6 x^3 - x, \text{ find } \frac{dy}{dx} at x = 1 .\]
For the function \[f(x) = \frac{x^{100}}{100} + \frac{x^{99}}{99} + . . . + \frac{x^2}{2} + x + 1 .\]
xn loga x
x2 sin x log x
(1 − 2 tan x) (5 + 4 sin x)
\[\frac{x^2 \cos\frac{\pi}{4}}{\sin x}\]
(2x2 − 3) sin x
\[\frac{e^x - \tan x}{\cot x - x^n}\]
\[\frac{x}{1 + \tan x}\]
\[\frac{x^2 - x + 1}{x^2 + x + 1}\]
\[\frac{\sqrt{a} + \sqrt{x}}{\sqrt{a} - \sqrt{x}}\]
\[\frac{1 + 3^x}{1 - 3^x}\]
\[\frac{\sec x - 1}{\sec x + 1}\]
\[\frac{x^5 - \cos x}{\sin x}\]
\[\frac{ax + b}{p x^2 + qx + r}\]
Write the value of \[\lim_{x \to c} \frac{f(x) - f(c)}{x - c}\]
Write the value of \[\lim_{x \to a} \frac{x f (a) - a f (x)}{x - a}\]
Write the value of \[\frac{d}{dx}\left( x \left| x \right| \right)\]
Mark the correct alternative in of the following:
If \[f\left( x \right) = \frac{x - 4}{2\sqrt{x}}\]
Mark the correct alternative in of the following:
If\[y = 1 + \frac{x}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + . . .\]then \[\frac{dy}{dx} =\]
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\[f\left( x \right) = 1 + x + \frac{x^2}{2} + . . . + \frac{x^{100}}{100}\] then \[f'\left( 1 \right)\] is equal to
Mark the correct alternative in each of the following:
If\[y = \frac{\sin x + \cos x}{\sin x - \cos x}\] then \[\frac{dy}{dx}\]at x = 0 is
(ax2 + cot x)(p + q cos x)
