Advertisements
Advertisements
Question
x−3 (5 + 3x)
Solution
\[\text{ Let } u = x^{- 3} ; v = \left( 5 + 3x \right)\]
\[\text{ Then }, u = - 3 x^{- 4} ; v' = 3\]
\[\text{ Using the product rule } :\]
\[\frac{d}{dx}\left( uv \right) = uv' + vu'\]
\[\frac{d}{dx}\left[ x^3 \left( 5 + 3x \right) \right] = x^{- 3} . 3 + \left( 5 + 3x \right) \left( - 3 x^{- 4} \right)\]
\[ = 3 x^{- 3} - 15 x^{- 4} - 9 x^{- 3} \]
\[ = - 15 x^{- 4} - 6 x^{- 3}\]
APPEARS IN
RELATED QUESTIONS
Find the derivative of 99x at x = 100.
Find the derivative of x at x = 1.
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)`
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):
`(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):
`4sqrtx - 2`
Find the derivative of f (x) = x2 − 2 at x = 10
Find the derivative of the following function at the indicated point:
sin 2x at x =\[\frac{\pi}{2}\]
\[\frac{x + 2}{3x + 5}\]
k xn
(x2 + 1) (x − 5)
\[\frac{2x + 3}{x - 2}\]
Differentiate of the following from first principle:
e3x
Differentiate of the following from first principle:
x sin x
Differentiate each of the following from first principle:
x2 ex
\[\cos \sqrt{x}\]
x4 − 2 sin x + 3 cos x
\[\frac{a \cos x + b \sin x + c}{\sin x}\]
Find the rate at which the function f (x) = x4 − 2x3 + 3x2 + x + 5 changes with respect to x.
(x3 + x2 + 1) sin x
x−4 (3 − 4x−5)
\[\frac{\sin x - x \cos x}{x \sin x + \cos x}\]
\[\frac{{10}^x}{\sin x}\]
\[\frac{1 + \log x}{1 - \log x}\]
\[\frac{a + b \sin x}{c + d \cos x}\]
\[\frac{x + \cos x}{\tan x}\]
\[\frac{1}{a x^2 + bx + c}\]
Write the value of \[\lim_{x \to a} \frac{x f (a) - a f (x)}{x - a}\]
Write the value of \[\frac{d}{dx}\left( x \left| x \right| \right)\]
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\[y = 1 + \frac{x}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + . . .\]then \[\frac{dy}{dx} =\]
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 \[f\left( x \right) = x^{100} + x^{99} + . . . + x + 1\] then \[f'\left( 1 \right)\] is equal to
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
Mark the correct alternative in of the following:
If f(x) = x sinx, then \[f'\left( \frac{\pi}{2} \right) =\]
Find the derivative of f(x) = tan(ax + b), by first principle.
