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 (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):
`(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):
sin (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):
cosec x cot 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):
`cos x/(1 + sin 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):
`(sin x + cos x)/(sin x - cos x)`
Find the derivative of f (x) = 3x at x = 2
Find the derivative of f (x) x at x = 1
Find the derivative of f (x) = tan x at x = 0
\[\frac{x + 2}{3x + 5}\]
Differentiate of the following from first principle:
− x
Differentiate of the following from first principle:
(−x)−1
Differentiate each of the following from first principle:
x2 sin x
Differentiate each of the following from first principle:
\[e^\sqrt{ax + b}\]
Differentiate each of the following from first principle:
\[3^{x^2}\]
tan 2x
\[\sin \sqrt{2x}\]
\[\log\left( \frac{1}{\sqrt{x}} \right) + 5 x^a - 3 a^x + \sqrt[3]{x^2} + 6 \sqrt[4]{x^{- 3}}\]
\[\text{ If } y = \left( \sin\frac{x}{2} + \cos\frac{x}{2} \right)^2 , \text{ find } \frac{dy}{dx} at x = \frac{\pi}{6} .\]
\[\text{ If } y = \left( \frac{2 - 3 \cos x}{\sin x} \right), \text{ find } \frac{dy}{dx} at x = \frac{\pi}{4}\]
Find the slope of the tangent to the curve f (x) = 2x6 + x4 − 1 at x = 1.
x3 ex
xn tan x
logx2 x
x3 ex cos x
x5 (3 − 6x−9)
x−4 (3 − 4x−5)
\[\frac{e^x - \tan x}{\cot x - x^n}\]
\[\frac{a x^2 + bx + c}{p x^2 + qx + r}\]
\[\frac{1 + 3^x}{1 - 3^x}\]
\[\frac{4x + 5 \sin x}{3x + 7 \cos x}\]
\[\frac{x^5 - \cos x}{\sin x}\]
\[\frac{x}{\sin^n x}\]
\[\frac{1}{a x^2 + bx + c}\]
Write the value of \[\lim_{x \to c} \frac{f(x) - f(c)}{x - c}\]
Write the value of the derivative of f (x) = |x − 1| + |x − 3| at x = 2.
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\[f\left( x \right) = 1 + x + \frac{x^2}{2} + . . . + \frac{x^{100}}{100}\] then \[f'\left( 1 \right)\] is equal to
Let f(x) = x – [x]; ∈ R, then f'`(1/2)` is ______.
