Advertisements
Advertisements
प्रश्न
\[\frac{1}{x^3}\]
Advertisements
उत्तर
\[ \frac{d}{dx}\left( f(x) \right) = \lim_{h \to 0} \frac{f\left( x + h \right) - f\left( x \right)}{h}\]
\[ = \lim_{h \to 0} \frac{\frac{1}{(x + h )^3} - \frac{1}{x^3}}{h}\]
\[ = \lim_{h \to 0} \frac{x^3 - (x + h )^3}{h(x + h )^3 x^3}\]
\[ = \lim_{h \to 0} \frac{x^3 - x^3 - 3 x^2 h - 3x h^2 - h^3}{h(x + h )^3 x^3}\]
\[ = \lim_{h \to 0} \frac{- 3 x^2 h - 3x h^2 - h^3}{h(x + h )^3 x^3}\]
\[ = \lim_{h \to 0} \frac{h\left( - 3 x^2 - 3xh - h^2 \right)}{h(x + h )^3 x^3}\]
\[ = \lim_{h \to 0} \frac{\left( - 3 x^2 - 3xh - h^2 \right)}{(x + h )^3 x^3}\]
\[ = \frac{- 3 x^2}{x^6}\]
\[ = \frac{- 3}{x^4}\]
\[ = - 3 x^{- 4} \]
\[\]
APPEARS IN
संबंधित प्रश्न
Find the derivative of x2 – 2 at x = 10.
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) (cx + d)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):
`(px^2 +qx + r)/(ax +b)`
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 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 the following function at the indicated point:
Find the derivative of the following function at the indicated point:
2 cos x at x =\[\frac{\pi}{2}\]
\[\frac{x + 1}{x + 2}\]
\[\frac{x + 2}{3x + 5}\]
(x2 + 1) (x − 5)
\[\frac{2x + 3}{x - 2}\]
Differentiate of the following from first principle:
− x
Differentiate of the following from first principle:
sin (x + 1)
Differentiate each of the following from first principle:
x2 sin x
Differentiate each of the following from first principle:
\[e^\sqrt{2x}\]
tan2 x
ex log a + ea long x + ea log a
(2x2 + 1) (3x + 2)
a0 xn + a1 xn−1 + a2 xn−2 + ... + an−1 x + an.
\[\log\left( \frac{1}{\sqrt{x}} \right) + 5 x^a - 3 a^x + \sqrt[3]{x^2} + 6 \sqrt[4]{x^{- 3}}\]
sin x cos x
\[\frac{2^x \cot x}{\sqrt{x}}\]
x4 (5 sin x − 3 cos x)
x5 (3 − 6x−9)
(ax + b) (a + d)2
\[\frac{e^x - \tan x}{\cot x - x^n}\]
\[\frac{1}{a x^2 + bx + c}\]
\[\frac{e^x + \sin x}{1 + \log x}\]
\[\frac{4x + 5 \sin x}{3x + 7 \cos x}\]
\[\frac{\sec x - 1}{\sec x + 1}\]
\[\frac{x^5 - \cos x}{\sin x}\]
If x < 2, then write the value of \[\frac{d}{dx}(\sqrt{x^2 - 4x + 4)}\]
Write the value of \[\frac{d}{dx}\left( \log \left| x \right| \right)\]
If f (1) = 1, f' (1) = 2, then write the value of \[\lim_{x \to 1} \frac{\sqrt{f (x)} - 1}{\sqrt{x} - 1}\]
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:
Let f(x) = x − [x], x ∈ R, then \[f'\left( \frac{1}{2} \right)\]
Find the derivative of f(x) = tan(ax + b), by first principle.
