Advertisements
Advertisements
प्रश्न
Mark the correct alternative in of the following:
If f(x) = x sinx, then \[f'\left( \frac{\pi}{2} \right) =\]
पर्याय
0
1
−1
\[\frac{1}{2}\]
Advertisements
उत्तर
f(x) = x sinx
Differentiating both sides with respect to x, we get
\[f'\left( x \right) = x \times \frac{d}{dx}\left( \sin x \right) + \sin x \times \frac{d}{dx}\left( x \right) \left( \text{ Product rule } \right)\]
\[ = x \times \cos x + \sin x \times 1\]
\[ = x \cos x + \sin x\]
Putting \[x = \frac{\pi}{2}\]
we get \[f'\left( \frac{\pi}{2} \right) = \frac{\pi}{2} \times \cos\left( \frac{\pi}{2} \right) + \sin\left( \frac{\pi}{2} \right)\]
\[ = \frac{\pi}{2} \times 0 + 1\]
\[ = 1\]
Hence, the correct answer is option (b).
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):
`(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):
`(ax + b)/(px^2 + qx + r)`
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) x at x = 1
Find the derivative of f (x) = tan 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 =\[\frac{\pi}{2}\]
\[\frac{1}{\sqrt{3 - x}}\]
x ex
Differentiate of the following from first principle:
\[\cos\left( x - \frac{\pi}{8} \right)\]
Differentiate of the following from first principle:
x sin x
Differentiate each of the following from first principle:
\[\sqrt{\sin 2x}\]
Differentiate each of the following from first principle:
\[\frac{\cos x}{x}\]
tan2 x
x4 − 2 sin x + 3 cos x
\[\left( x + \frac{1}{x} \right)\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)\]
\[\frac{( x^3 + 1)(x - 2)}{x^2}\]
\[If y = \sqrt{\frac{x}{a}} + \sqrt{\frac{a}{x}}, \text{ prove that } 2xy\frac{dy}{dx} = \left( \frac{x}{a} - \frac{a}{x} \right)\]
For the function \[f(x) = \frac{x^{100}}{100} + \frac{x^{99}}{99} + . . . + \frac{x^2}{2} + x + 1 .\]
sin x cos x
x2 sin x log x
(1 − 2 tan x) (5 + 4 sin x)
sin2 x
x4 (5 sin x − 3 cos x)
(ax + b) (a + d)2
\[\frac{x + e^x}{1 + \log x}\]
\[\frac{\sin x - x \cos x}{x \sin x + \cos x}\]
\[\frac{x^2 - x + 1}{x^2 + x + 1}\]
\[\frac{x + \cos x}{\tan x}\]
\[\frac{ax + b}{p x^2 + qx + r}\]
\[\frac{1}{a x^2 + bx + c}\]
Write the value of \[\lim_{x \to a} \frac{x f (a) - a f (x)}{x - a}\]
If x < 2, then write the value of \[\frac{d}{dx}(\sqrt{x^2 - 4x + 4)}\]
Mark the correct alternative in of the following:
If \[y = \sqrt{x} + \frac{1}{\sqrt{x}}\] then \[\frac{dy}{dx}\] at x = 1 is
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
