Advertisements
Advertisements
प्रश्न
sin x cos x
उत्तर
\[\text{ Let } u = \sin x; v = \cos x\]
\[\text{ Then }, u' = \cos x; v' = - \sin x\]
\[\text{ Using theproduct rule }:\]
\[\frac{d}{dx}\left( uv \right) = uv' + vu'\]
\[\frac{d}{dx}\left( \sin x \cos x \right) = \sin x \left( - \sin x \right) + \cos x . \cos x\]
\[ = - \sin^2 x + \cos^2 x\]
\[ = \cos 2x\]
APPEARS IN
संबंधित प्रश्न
Find the derivative of 99x at x = 100.
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):
cosec x cot 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):
`(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):
x4 (5 sin x – 3 cos x)
Find the derivative of f (x) = 3x at x = 2
Find the derivative of f (x) = tan x at x = 0
Find the derivative of the following function at the indicated point:
\[\frac{1}{x^3}\]
\[\frac{1}{\sqrt{3 - x}}\]
(x2 + 1) (x − 5)
\[\sqrt{2 x^2 + 1}\]
Differentiate of the following from first principle:
− x
Differentiate each of the following from first principle:
\[\sqrt{\sin 2x}\]
Differentiate each of the following from first principle:
\[e^\sqrt{ax + b}\]
tan (2x + 1)
\[\sqrt{\tan x}\]
\[\tan \sqrt{x}\]
log3 x + 3 loge x + 2 tan x
\[If y = \sqrt{\frac{x}{a}} + \sqrt{\frac{a}{x}}, \text{ prove that } 2xy\frac{dy}{dx} = \left( \frac{x}{a} - \frac{a}{x} \right)\]
If for f (x) = λ x2 + μ x + 12, f' (4) = 15 and f' (2) = 11, then find λ and μ.
x−4 (3 − 4x−5)
Differentiate in two ways, using product rule and otherwise, the function (1 + 2 tan x) (5 + 4 cos x). Verify that the answers are the same.
\[\frac{a x^2 + bx + c}{p x^2 + qx + r}\]
\[\frac{e^x + \sin x}{1 + \log x}\]
\[\frac{\sin x - x \cos x}{x \sin x + \cos x}\]
\[\frac{1 + \log x}{1 - \log x}\]
\[\frac{a + b \sin x}{c + d \cos x}\]
\[\frac{ax + b}{p x^2 + qx + r}\]
\[\frac{1}{a x^2 + bx + c}\]
Write the value of \[\lim_{x \to c} \frac{f(x) - f(c)}{x - c}\]
Write the value of \[\lim_{x \to a} \frac{x f (a) - a f (x)}{x - a}\]
If x < 2, then write the value of \[\frac{d}{dx}(\sqrt{x^2 - 4x + 4)}\]
If |x| < 1 and y = 1 + x + x2 + x3 + ..., then write the value of \[\frac{dy}{dx}\]
Mark the correct alternative in each of the following:
If\[f\left( x \right) = \frac{x^n - a^n}{x - a}\] then \[f'\left( a \right)\]
