Advertisements
Advertisements
प्रश्न
Find the derivative of the following function at the indicated point:
Advertisements
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 99x at x = 100.
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):
`a/x^4 = b/x^2 + 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):
(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 + 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):
`(a + bsin x)/(c + dcosx)`
Find the derivative of f (x) = 3x at x = 2
\[\frac{1}{x^3}\]
Differentiate of the following from first principle:
− x
Differentiate each of the following from first principle:
\[\frac{\cos x}{x}\]
Differentiate each of the following from first principle:
x2 sin x
Differentiate each of the following from first principle:
x2 ex
Differentiate each of the following from first principle:
\[e^{x^2 + 1}\]
tan2 x
tan 2x
\[\tan \sqrt{x}\]
log3 x + 3 loge x + 2 tan x
\[\frac{2 x^2 + 3x + 4}{x}\]
\[\frac{( x^3 + 1)(x - 2)}{x^2}\]
\[\frac{(x + 5)(2 x^2 - 1)}{x}\]
\[\text{ If } y = \left( \frac{2 - 3 \cos x}{\sin x} \right), \text{ find } \frac{dy}{dx} at x = \frac{\pi}{4}\]
x3 sin x
Differentiate each of the following functions by the product rule and the other method and verify that answer from both the methods is the same.
(3x2 + 2)2
Differentiate each of the following functions by the product rule and the other method and verify that answer from both the methods is the same.
(x + 2) (x + 3)
(ax + b) (a + d)2
\[\frac{a + b \sin x}{c + d \cos x}\]
\[\frac{x}{\sin^n x}\]
\[\frac{ax + b}{p x^2 + qx + r}\]
Write the value of \[\frac{d}{dx} \left\{ \left( x + \left| x \right| \right) \left| x \right| \right\}\]
If f (x) = \[\frac{x^2}{\left| x \right|},\text{ write }\frac{d}{dx}\left( f (x) \right)\]
Write the derivative of f (x) = 3 |2 + x| at x = −3.
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 \[f\left( x \right) = \frac{x - 4}{2\sqrt{x}}\]
Find the derivative of 2x4 + x.
Find the derivative of x2 cosx.
