Advertisements
Advertisements
Question
(x3 + x2 + 1) sin x
Solution
\[\text{ Let } u = x^3 + x^2 + 1; v = \sin x\]
\[\text{ Then }, u' = 3 x^2 + 2x; v' = \cos x\]
\[\text{ By product rule },\]
\[\frac{d}{dx}\left( uv \right) = uv' + vu'\]
\[\frac{d}{dx}\left[ \left( x^3 + x^2 + 1 \right) \sin x \right] = \left( x^3 + x^2 + 1 \right) \cos x + \left( 3 x^2 + 2x \right) \sin x \]
\[\]
APPEARS IN
RELATED QUESTIONS
Find the derivative of `2x - 3/4`
Find the derivative of x–3 (5 + 3x).
Find the derivative of x–4 (3 – 4x–5).
Find the derivative of `2/(x + 1) - x^2/(3x -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):
`(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):
`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):
`(sin x + cos x)/(sin x - cos x)`
Find the derivative of f (x) = tan x at x = 0
Find the derivative of the following function at the indicated point:
sin 2x at x =\[\frac{\pi}{2}\]
\[\frac{x^2 + 1}{x}\]
(x2 + 1) (x − 5)
\[\sqrt{2 x^2 + 1}\]
x ex
Differentiate each of the following from first principle:
x2 sin x
Differentiate each of the following from first principle:
\[\sqrt{\sin (3x + 1)}\]
Differentiate each of the following from first principle:
x2 ex
Differentiate each of the following from first principle:
\[e^\sqrt{ax + b}\]
\[\sqrt{\tan x}\]
\[\tan \sqrt{x}\]
\[\text{ If } y = \frac{2 x^9}{3} - \frac{5}{7} x^7 + 6 x^3 - x, \text{ find } \frac{dy}{dx} at x = 1 .\]
x3 ex
xn loga x
x2 sin x log x
logx2 x
\[\frac{x^2 \cos\frac{\pi}{4}}{\sin x}\]
x4 (5 sin x − 3 cos x)
x−4 (3 − 4x−5)
(ax + b)n (cx + d)n
\[\frac{2^x \cot x}{\sqrt{x}}\]
\[\frac{4x + 5 \sin x}{3x + 7 \cos x}\]
Write the value of \[\lim_{x \to c} \frac{f(x) - f(c)}{x - c}\]
Write the value of \[\frac{d}{dx}\left( x \left| x \right| \right)\]
If f (1) = 1, f' (1) = 2, then write the value of \[\lim_{x \to 1} \frac{\sqrt{f (x)} - 1}{\sqrt{x} - 1}\]
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
Find the derivative of x2 cosx.
Find the derivative of f(x) = tan(ax + b), by first principle.
`(a + b sin x)/(c + d cos x)`
