Advertisements
Advertisements
प्रश्न
Find the derivative of the following function at the indicated point:
उत्तर
x at x = 1
\[\left( ii \right) \hspace{0.167em}\text{ We have }: \]
\[f'(x) = \lim_{h \to 0} \frac{f(1 + h) - f(1)}{h}\]
\[ = \lim_{h \to 0} \frac{1 + h - 1}{h}\]
\[ = \lim_{h \to 0} 1\]
\[ = 1\]
APPEARS IN
संबंधित प्रश्न
Find the derivative of x at x = 1.
For the function
f(x) = `x^100/100 + x^99/99 + ...+ x^2/2 + x + 1`
Prove that f'(1) = 100 f'(0)
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):
`(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):
(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):
`cos x/(1 + sin 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):
sinn x
Find the derivative of f (x) = x2 − 2 at x = 10
Find the derivative of the following function at the indicated point:
sin x at x =\[\frac{\pi}{2}\]
k xn
Differentiate each of the following from first principle:
e−x
Differentiate of the following from first principle:
eax + b
Differentiate of the following from first principle:
(−x)−1
Differentiate each of the following from first principle:
x2 sin x
Differentiate each of the following from first principle:
sin x + cos x
Differentiate each of the following from first principle:
\[e^{x^2 + 1}\]
\[\tan \sqrt{x}\]
(2x2 + 1) (3x + 2)
\[\frac{1}{\sin x} + 2^{x + 3} + \frac{4}{\log_x 3}\]
If for f (x) = λ x2 + μ x + 12, f' (4) = 15 and f' (2) = 11, then find λ and μ.
sin x cos x
x3 ex cos x
x−4 (3 − 4x−5)
\[\frac{x}{1 + \tan x}\]
\[\frac{1}{a x^2 + bx + c}\]
\[\frac{\sqrt{a} + \sqrt{x}}{\sqrt{a} - \sqrt{x}}\]
\[\frac{{10}^x}{\sin x}\]
\[\frac{1 + \log x}{1 - \log x}\]
\[\frac{4x + 5 \sin x}{3x + 7 \cos x}\]
\[\frac{x}{1 + \tan x}\]
\[\frac{x}{\sin^n x}\]
If x < 2, then write the value of \[\frac{d}{dx}(\sqrt{x^2 - 4x + 4)}\]
Write the value of \[\frac{d}{dx} \left\{ \left( x + \left| x \right| \right) \left| x \right| \right\}\]
If f (1) = 1, f' (1) = 2, then write the value of \[\lim_{x \to 1} \frac{\sqrt{f (x)} - 1}{\sqrt{x} - 1}\]
Mark the correct alternative in of the following:
If \[f\left( x \right) = x^{100} + x^{99} + . . . + x + 1\] then \[f'\left( 1 \right)\] is equal to
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 2x4 + x.
Let f(x) = x – [x]; ∈ R, then f'`(1/2)` is ______.
