Advertisements
Advertisements
प्रश्न
tan (2x + 1)
Advertisements
उत्तर
\[\frac{d}{dx}\left( f(x) \right) = \lim_{h \to 0} \frac{f\left( x + h \right) - f\left( x \right)}{h}\]
\[ = \lim_{h \to 0} \frac{\tan \left( 2x + 2h + 1 \right) - \tan \left( 2x + 1 \right)}{h}\]
\[ = \lim_{h \to 0} \frac{\frac{sin \left( 2x + 2h + 1 \right)}{\cos \left( 2x + 2h + 1 \right)} - \frac{\sin \left( 2x + 1 \right)}{\cos \left( 2x + 1 \right)}}{h}\]
\[ = \lim_{h \to 0} \frac{sin \left( 2x + 2h + 1 \right) \cos \left( 2x + 1 \right) - \cos \left( 2x + 2h + 1 \right) \sin \left( 2x + 1 \right)}{h \cos \left( 2x + 2h + 1 \right) \cos \left( 2x + 1 \right)}\]
\[ = \lim_{h \to 0} \frac{\sin \left( 2x + 2h + 1 - 2x - 1 \right)}{h \cos \left( 2x + 2h + 1 \right) \cos \left( 2x + 1 \right)}\]
\[ = \frac{1}{\cos \left( 2x + 1 \right)} \lim_{h \to 0} \frac{\sin \left( 2h \right)}{2h} \times 2 \lim_{h \to 0} \frac{1}{\cos \left( 2x + 2h + 1 \right)}\]
\[ = \frac{1}{\cos \left( 2x + 1 \right)} \times 2 \times \frac{1}{\cos \left( 2x + 1 \right)}\]
\[ = \frac{2}{\cos^2 \left( 2x + 1 \right)}\]
\[ = 2 \sec^2 \left( 2x + 1 \right)\]
APPEARS IN
संबंधित प्रश्न
Find the derivative of x–4 (3 – 4x–5).
Find the derivative of `2/(x + 1) - x^2/(3x -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):
`(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)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):
`(px^2 +qx + r)/(ax +b)`
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)n (cx + d)m
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 the following function at the indicated point:
2 cos x at x =\[\frac{\pi}{2}\]
\[\frac{1}{x^3}\]
k xn
(x2 + 1) (x − 5)
Differentiate of the following from first principle:
eax + b
Differentiate of the following from first principle:
sin (x + 1)
Differentiate of the following from first principle:
sin (2x − 3)
Differentiate each of the following from first principle:
\[\sqrt{\sin (3x + 1)}\]
tan2 x
\[\frac{a \cos x + b \sin x + c}{\sin x}\]
\[\text{ If } y = \left( \frac{2 - 3 \cos x}{\sin x} \right), \text{ find } \frac{dy}{dx} at x = \frac{\pi}{4}\]
\[If y = \sqrt{\frac{x}{a}} + \sqrt{\frac{a}{x}}, \text{ prove that } 2xy\frac{dy}{dx} = \left( \frac{x}{a} - \frac{a}{x} \right)\]
x2 sin x log x
sin2 x
\[e^x \log \sqrt{x} \tan x\]
(ax + b)n (cx + d)n
\[\frac{e^x - \tan x}{\cot x - x^n}\]
\[\frac{3^x}{x + \tan x}\]
\[\frac{1 + \log x}{1 - \log x}\]
\[\frac{p x^2 + qx + r}{ax + b}\]
Write the value of \[\lim_{x \to c} \frac{f(x) - f(c)}{x - c}\]
Write the value of the derivative of f (x) = |x − 1| + |x − 3| at x = 2.
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\[y = 1 + \frac{x}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + . . .\]then \[\frac{dy}{dx} =\]
Mark the correct alternative in of the following:
If \[y = \sqrt{x} + \frac{1}{\sqrt{x}}\] then \[\frac{dy}{dx}\] at x = 1 is
Mark the correct alternative in each of the following:
If\[f\left( x \right) = \frac{x^n - a^n}{x - a}\] then \[f'\left( a \right)\]
Find the derivative of x2 cosx.
Find the derivative of f(x) = tan(ax + b), by first principle.
