Advertisements
Advertisements
प्रश्न
(x + 2)3
Advertisements
उत्तर
\[\frac{d}{dx}\left( f(x) \right) = \lim_{h \to 0} \frac{f\left( x + h \right) - f\left( x \right)}{h}\]
\[ = \lim_{h \to 0} \frac{\left( x + h + 2 \right)^3 - \left( x + 2 \right)^3}{h}\]
\[ = \lim_{h \to 0} \frac{\left( x + h + 2 - x - 2 \right)\left[ \left( x + h + 2 \right)^2 + \left( x + h + 2 \right)\left( x + 2 \right) + \left( x + 2 \right)^2 \right]}{h}\]
\[ = \lim_{h \to 0} \frac{h\left[ \left( x + h + 2 \right)^2 + \left( x + h + 2 \right)\left( x + 2 \right) + \left( x + 2 \right)^2 \right]}{h}\]
\[ = \lim_{h \to 0} \left[ \left( x + h + 2 \right)^2 + \left( x + h + 2 \right)\left( x + 2 \right) + \left( x + 2 \right)^2 \right]\]
\[ = \left[ \left( x + 0 + 2 \right)^2 + \left( x + 0 + 2 \right)\left( x + 2 \right) + \left( x + 2 \right)^2 \right]\]
\[ = \left( x + 2 \right)^2 + \left( x + 2 \right)^2 + \left( x + 2 \right)^2 \]
\[ = 3 \left( x + 2 \right)^2\]
APPEARS IN
संबंधित प्रश्न
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):
`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):
`4sqrtx - 2`
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):
x4 (5 sin x – 3 cos x)
Find the derivative of f (x) x at x = 1
Find the derivative of f (x) = cos x at x = 0
Find the derivative of the following function at the indicated point:
k xn
(x2 + 1) (x − 5)
Differentiate of the following from first principle:
x sin x
Differentiate each of the following from first principle:
\[\sqrt{\sin (3x + 1)}\]
Differentiate each of the following from first principle:
sin x + cos x
Differentiate each of the following from first principle:
\[e^\sqrt{2x}\]
Differentiate each of the following from first principle:
\[e^\sqrt{ax + b}\]
\[\tan \sqrt{x}\]
\[\frac{x^3}{3} - 2\sqrt{x} + \frac{5}{x^2}\]
a0 xn + a1 xn−1 + a2 xn−2 + ... + an−1 x + an.
\[\frac{1}{\sin x} + 2^{x + 3} + \frac{4}{\log_x 3}\]
cos (x + a)
If for f (x) = λ x2 + μ x + 12, f' (4) = 15 and f' (2) = 11, then find λ and μ.
(x sin x + cos x) (x cos x − 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
\[\frac{e^x}{1 + x^2}\]
\[\frac{e^x + \sin x}{1 + \log x}\]
\[\frac{x}{1 + \tan x}\]
\[\frac{x}{\sin^n x}\]
Write the value of \[\lim_{x \to c} \frac{f(x) - f(c)}{x - c}\]
If \[\frac{\pi}{2}\] then find \[\frac{d}{dx}\left( \sqrt{\frac{1 + \cos 2x}{2}} \right)\]
Write the value of the derivative of f (x) = |x − 1| + |x − 3| at x = 2.
If f (1) = 1, f' (1) = 2, then write the value of \[\lim_{x \to 1} \frac{\sqrt{f (x)} - 1}{\sqrt{x} - 1}\]
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\[y = 1 + \frac{x}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + . . .\]then \[\frac{dy}{dx} =\]
Mark the correct alternative in each of the following:
If\[y = \frac{\sin x + \cos x}{\sin x - \cos x}\] then \[\frac{dy}{dx}\]at x = 0 is
(ax2 + cot x)(p + q cos x)
