Advertisements
Advertisements
Question
\[\frac{(x + 5)(2 x^2 - 1)}{x}\]
Advertisements
Solution
\[\frac{d}{dx}\left( \frac{\left( x + 5 \right)\left( 2 x^2 - 1 \right)}{x} \right)\]
\[ = \frac{d}{dx}\left( \frac{2 x^3 + 10 x^2 - x - 5}{x} \right)\]
\[ = \frac{d}{dx}\left( \frac{2 x^3}{x} \right) + \frac{d}{dx}\left( \frac{10 x^2}{x} \right) - \frac{d}{dx}\left( \frac{x}{x} \right) - \frac{d}{dx}\left( \frac{5}{x} \right)\]
\[ = 2\frac{d}{dx}\left( x^2 \right) + 10\frac{d}{dx}\left( x \right) - \frac{d}{dx}\left( 1 \right) - 5\frac{d}{dx}\left( x^{- 1} \right)\]
\[ = 2\left( 2x \right) + 10\left( 1 \right) - 0 - 5\left( - 1 \right) x^{- 2} \]
\[ = 4x + 10 + \frac{5}{x^2}\]
APPEARS IN
RELATED QUESTIONS
Find the derivative of 99x at x = 100.
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–4 (3 – 4x–5).
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):
`(sin(x + a))/ cos x`
\[\frac{x^2 + 1}{x}\]
\[\frac{x^2 - 1}{x}\]
\[\frac{x + 1}{x + 2}\]
(x2 + 1) (x − 5)
\[\sqrt{2 x^2 + 1}\]
x ex
Differentiate of the following from first principle:
sin (x + 1)
Differentiate each of the following from first principle:
\[\frac{\sin x}{x}\]
3x + x3 + 33
(2x2 + 1) (3x + 2)
\[\text{ If } y = \left( \sin\frac{x}{2} + \cos\frac{x}{2} \right)^2 , \text{ find } \frac{dy}{dx} at x = \frac{\pi}{6} .\]
\[\text{ If } y = \left( \frac{2 - 3 \cos x}{\sin x} \right), \text{ find } \frac{dy}{dx} at x = \frac{\pi}{4}\]
For the function \[f(x) = \frac{x^{100}}{100} + \frac{x^{99}}{99} + . . . + \frac{x^2}{2} + x + 1 .\]
x3 ex
x5 (3 − 6x−9)
\[\frac{x + e^x}{1 + \log x}\]
\[\frac{a x^2 + bx + c}{p x^2 + qx + r}\]
\[\frac{\sqrt{a} + \sqrt{x}}{\sqrt{a} - \sqrt{x}}\]
\[\frac{1 + \log x}{1 - \log x}\]
\[\frac{a + b \sin x}{c + d \cos x}\]
\[\frac{p x^2 + qx + r}{ax + b}\]
\[\frac{ax + b}{p x^2 + qx + r}\]
\[\frac{1}{a x^2 + bx + c}\]
If f (x) = \[\frac{x^2}{\left| x \right|},\text{ write }\frac{d}{dx}\left( f (x) \right)\]
Write the value of \[\frac{d}{dx}\left( \log \left| x \right| \right)\]
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 \[f\left( x \right) = \frac{x - 4}{2\sqrt{x}}\]
Mark the correct alternative in of the following:
If \[y = \frac{1 + \frac{1}{x^2}}{1 - \frac{1}{x^2}}\] then \[\frac{dy}{dx} =\]
(ax2 + cot x)(p + q cos x)
Let f(x) = x – [x]; ∈ R, then f'`(1/2)` is ______.
