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 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):
`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
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 f (x) = 99x at x = 100
Find the derivative of f (x) x at x = 1
x2 + x + 3
\[\sqrt{2 x^2 + 1}\]
Differentiate of the following from first principle:
eax + b
Differentiate of the following from first principle:
− x
Differentiate of the following from first principle:
\[\cos\left( x - \frac{\pi}{8} \right)\]
Differentiate of the following from first principle:
sin (2x − 3)
Differentiate each of the following from first principle:
\[e^\sqrt{ax + b}\]
Differentiate each of the following from first principle:
\[3^{x^2}\]
tan 2x
\[\tan \sqrt{x}\]
\[\tan \sqrt{x}\]
3x + x3 + 33
log3 x + 3 loge x + 2 tan x
\[\text{ If } y = \left( \frac{2 - 3 \cos x}{\sin x} \right), \text{ find } \frac{dy}{dx} at x = \frac{\pi}{4}\]
Find the slope of the tangent to the curve f (x) = 2x6 + x4 − 1 at x = 1.
x3 sin x
xn loga x
(x sin x + cos x) (x cos x − sin x)
\[\frac{x^2 \cos\frac{\pi}{4}}{\sin x}\]
x−3 (5 + 3x)
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)
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.
(3 sec x − 4 cosec x) (−2 sin x + 5 cos x)
\[\frac{x^2 + 1}{x + 1}\]
\[\frac{x^2 - x + 1}{x^2 + x + 1}\]
\[\frac{a + \sin x}{1 + a \sin x}\]
\[\frac{3^x}{x + \tan x}\]
\[\frac{1}{a x^2 + bx + c}\]
If \[\frac{\pi}{2}\] then find \[\frac{d}{dx}\left( \sqrt{\frac{1 + \cos 2x}{2}} \right)\]
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 of the following:
If \[y = \frac{\sin\left( x + 9 \right)}{\cos x}\] then \[\frac{dy}{dx}\] at x = 0 is
Mark the correct alternative in each of the following:
If\[f\left( x \right) = \frac{x^n - a^n}{x - a}\] then \[f'\left( a \right)\]
Mark the correct alternative in of the following:
If f(x) = x sinx, then \[f'\left( \frac{\pi}{2} \right) =\]
(ax2 + cot x)(p + q cos x)