Advertisements
Advertisements
प्रश्न
Find the derivative of f (x) = 3x at x = 2
Advertisements
उत्तर
We have:
\[{f'(2) = \lim}_{h \to 0} \frac{f(2 + h) - f(2)}{h}\]
\[ = \lim_{h \to 0} \frac{3(2 + h) - 3(2)}{h}\]
\[ = \lim_{h \to 0} \frac{6 + 3h - 6}{h}\]
\[ = \lim_{h \to 0} \frac{3h}{h}\]
\[ = 3\]
APPEARS IN
संबंधित प्रश्न
Find the derivative of `2x - 3/4`
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):
(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):
sin (x + a)
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 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 + a))/ cos x`
Find the derivative of the following function at the indicated point:
sin 2x at x =\[\frac{\pi}{2}\]
Differentiate each of the following from first principle:
\[\sqrt{\sin 2x}\]
a0 xn + a1 xn−1 + a2 xn−2 + ... + an−1 x + an.
\[\frac{1}{\sin x} + 2^{x + 3} + \frac{4}{\log_x 3}\]
\[\text{ If } y = \left( \frac{2 - 3 \cos x}{\sin x} \right), \text{ find } \frac{dy}{dx} at x = \frac{\pi}{4}\]
Find the slope of the tangent to the curve f (x) = 2x6 + x4 − 1 at x = 1.
\[\text{ If } y = \frac{2 x^9}{3} - \frac{5}{7} x^7 + 6 x^3 - x, \text{ find } \frac{dy}{dx} at x = 1 .\]
If for f (x) = λ x2 + μ x + 12, f' (4) = 15 and f' (2) = 11, then find λ and μ.
x3 sin x
x3 ex
xn loga x
\[\frac{2^x \cot x}{\sqrt{x}}\]
x5 ex + x6 log x
(x sin x + cos x) (x cos x − sin x)
logx2 x
x−3 (5 + 3x)
(ax + b) (a + d)2
(ax + b)n (cx + d)n
\[\frac{x^2 + 1}{x + 1}\]
\[\frac{x + e^x}{1 + \log x}\]
\[\frac{e^x - \tan x}{\cot x - x^n}\]
\[\frac{x \tan x}{\sec x + \tan x}\]
\[\frac{{10}^x}{\sin x}\]
\[\frac{1}{a x^2 + bx + c}\]
Write the value of \[\lim_{x \to a} \frac{x f (a) - a f (x)}{x - a}\]
If f (x) = |x| + |x−1|, write the value of \[\frac{d}{dx}\left( f (x) \right)\]
Mark the correct alternative in of the following:
Let f(x) = x − [x], x ∈ R, then \[f'\left( \frac{1}{2} \right)\]
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 \[y = \frac{\sin\left( x + 9 \right)}{\cos x}\] then \[\frac{dy}{dx}\] at x = 0 is
Find the derivative of f(x) = tan(ax + b), by first principle.
