Advertisements
Advertisements
प्रश्न
(x2 + 1) (x − 5)
Advertisements
उत्तर
\[ \left( x^2 + 1 \right)\left( x - 5 \right) = x^3 - 5 x^2 + x - 5\]
\[\frac{d}{dx}\left( f(x) \right) = \lim_{h \to 0} \frac{f\left( x + h \right) - f\left( x \right)}{h}\]
\[ = \lim_{h \to 0} \frac{\left( x + h \right)^3 - 5 \left( x + h \right)^2 + \left( x + h \right) - 5 - \left( x^3 - 5 x^2 + x - 5 \right)}{h}\]
\[ = \lim_{h \to 0} \frac{x^3 + 3 x^2 h + 3x h^2 + h^3 - 5 x^2 - 5 h^2 - 10xh + x + h - 5 - x^3 + 5 x^2 - x + 5}{h}\]
\[ = \lim_{h \to 0} \frac{3 x^2 h + 3x h^2 + h^3 - 5 h^2 - 10xh + h}{h}\]
\[ = \lim_{h \to 0} \frac{h \left( 3 x^2 + 3xh + h^2 - 5h - 10x + 1 \right)}{h}\]
\[ = \lim_{h \to 0} \left( 3 x^2 + 3xh + h^2 - 5h - 10x + 1 \right)\]
\[ = 3 x^2 - 10x + 1\]
APPEARS IN
संबंधित प्रश्न
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 x–3 (5 + 3x).
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):
(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):
`(1 + 1/x)/(1- 1/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):
`1/(ax^2 + bx + c)`
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) = x2 − 2 at x = 10
Find the derivative of the following function at the indicated point:
2 cos x at x =\[\frac{\pi}{2}\]
\[\frac{2}{x}\]
\[\frac{x^2 + 1}{x}\]
\[\frac{x + 1}{x + 2}\]
Differentiate of the following from first principle:
(−x)−1
Differentiate each of the following from first principle:
\[\sqrt{\sin 2x}\]
Differentiate each of the following from first principle:
\[\sqrt{\sin (3x + 1)}\]
tan (2x + 1)
\[\sqrt{\tan x}\]
\[\tan \sqrt{x}\]
3x + x3 + 33
\[\left( x + \frac{1}{x} \right)\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)\]
\[\frac{1}{\sin x} + 2^{x + 3} + \frac{4}{\log_x 3}\]
If for f (x) = λ x2 + μ x + 12, f' (4) = 15 and f' (2) = 11, then find λ and μ.
(x3 + x2 + 1) sin x
(x sin x + cos x) (x cos x − sin x)
(x sin x + cos x ) (ex + x2 log x)
(1 +x2) cos x
\[e^x \log \sqrt{x} \tan x\]
(ax + b)n (cx + d)n
\[\frac{2x - 1}{x^2 + 1}\]
\[\frac{x \tan x}{\sec x + \tan x}\]
\[\frac{a + b \sin x}{c + d \cos x}\]
\[\frac{\sec x - 1}{\sec x + 1}\]
\[\frac{x^5 - \cos x}{\sin x}\]
Write the value of \[\frac{d}{dx}\left( x \left| x \right| \right)\]
Write the value of \[\frac{d}{dx} \left\{ \left( x + \left| x \right| \right) \left| x \right| \right\}\]
Write the derivative of f (x) = 3 |2 + x| at x = −3.
If |x| < 1 and y = 1 + x + x2 + x3 + ..., then write the value of \[\frac{dy}{dx}\]
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 of the following:
If \[y = \frac{\sin\left( x + 9 \right)}{\cos x}\] then \[\frac{dy}{dx}\] at x = 0 is
