Advertisements
Advertisements
Question
x3 sin x
Advertisements
Solution
\[\text{ Let } u = x^3 ; v = \sin x\]
\[\text{ Then }, u' = 3 x^2 ; v' = \cos x\]
\[\text{ Using the product rule }:\]
\[\frac{d}{dx}\left( uv \right) = uv' + vu'\]
\[\frac{d}{dx}\left( x^3 \sin x \right) = x^3 \cos x + \sin x \left( 3 x^2 \right)\]
\[ = x^2 \left( x \cos x + 3 \sin x \right)\]
APPEARS IN
RELATED QUESTIONS
Find the derivative of 99x at x = 100.
Find the derivative of (5x3 + 3x – 1) (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):
(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):
`(px+ q) (r/s + s)`
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):
`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):
(ax + b)n
Find the derivative of f (x) = cos x at x = 0
Find the derivative of the following function at the indicated point:
sin x at x =\[\frac{\pi}{2}\]
\[\frac{x^2 - 1}{x}\]
k xn
\[\sqrt{2 x^2 + 1}\]
Differentiate of the following from first principle:
− x
Differentiate of the following from first principle:
x cos x
Differentiate each of the following from first principle:
\[\frac{\cos x}{x}\]
3x + x3 + 33
\[\left( x + \frac{1}{x} \right)\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)\]
\[\frac{2 x^2 + 3x + 4}{x}\]
2 sec x + 3 cot x − 4 tan x
\[\text{ If } y = \frac{2 x^9}{3} - \frac{5}{7} x^7 + 6 x^3 - x, \text{ find } \frac{dy}{dx} at x = 1 .\]
sin2 x
x−3 (5 + 3x)
Differentiate in two ways, using product rule and otherwise, the function (1 + 2 tan x) (5 + 4 cos x). Verify that the answers are the same.
(ax + b) (a + d)2
(ax + b)n (cx + d)n
\[\frac{2x - 1}{x^2 + 1}\]
\[\frac{x}{1 + \tan x}\]
\[\frac{1}{a x^2 + bx + c}\]
\[\frac{e^x + \sin x}{1 + \log x}\]
\[\frac{2^x \cot x}{\sqrt{x}}\]
\[\frac{x^2 - x + 1}{x^2 + x + 1}\]
\[\frac{x}{1 + \tan x}\]
Write the derivative of f (x) = 3 |2 + x| at x = −3.
If f (x) = \[\log_{x_2}\]write the value of f' (x).
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.
