Advertisements
Advertisements
Question
(x3 + x2 + 1) sin x
Advertisements
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 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):
`(sin(x + a))/ cos x`
Find the derivative of f (x) = x2 − 2 at x = 10
Find the derivative of f (x) x at x = 1
\[\frac{1}{x^3}\]
\[\frac{x^2 - 1}{x}\]
\[\frac{x + 1}{x + 2}\]
\[\frac{x + 2}{3x + 5}\]
x2 + x + 3
(x2 + 1) (x − 5)
Differentiate of the following from first principle:
e3x
Differentiate of the following from first principle:
sin (x + 1)
Differentiate of the following from first principle:
sin (2x − 3)
Differentiate each of the following from first principle:
\[e^\sqrt{ax + b}\]
tan (2x + 1)
tan 2x
\[\sin \sqrt{2x}\]
\[\cos \sqrt{x}\]
(2x2 + 1) (3x + 2)
\[\frac{( x^3 + 1)(x - 2)}{x^2}\]
\[If y = \sqrt{\frac{x}{a}} + \sqrt{\frac{a}{x}}, \text{ prove that } 2xy\frac{dy}{dx} = \left( \frac{x}{a} - \frac{a}{x} \right)\]
\[\text{ If } y = \frac{2 x^9}{3} - \frac{5}{7} x^7 + 6 x^3 - x, \text{ find } \frac{dy}{dx} at x = 1 .\]
x2 ex log x
\[\frac{x^2 \cos\frac{\pi}{4}}{\sin x}\]
x4 (5 sin x − 3 cos x)
Differentiate each of the following functions by the product rule and the other method and verify that answer from both the methods is the same.
(3x2 + 2)2
(ax + b)n (cx + d)n
\[\frac{{10}^x}{\sin x}\]
\[\frac{3^x}{x + \tan x}\]
\[\frac{x + \cos x}{\tan x}\]
\[\frac{x}{\sin^n x}\]
Write the value of \[\frac{d}{dx}\left( x \left| x \right| \right)\]
If f (x) = \[\frac{x^2}{\left| x \right|},\text{ write }\frac{d}{dx}\left( f (x) \right)\]
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 \[f'\left( \frac{1}{2} \right)\]
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
