Advertisements
Advertisements
Question
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.
(x + 2) (x + 3)
Advertisements
Solution
\[{\text{ Product rule } (1}^{st} \text{ method }):\]
\[\text{ Let } u = x + 2; v = x + 3\]
\[\text{ Then }, u' = 1; v' = 1\]
\[\text{ Using the product rule }:\]
\[\frac{d}{dx}\left( uv \right) = uv' + vu'\]
\[\frac{d}{dx}\left[ \left( x + 2 \right)\left( x + 3 \right) \right] = \left( x + 2 \right)1 + \left( x + 3 \right)1\]
\[ = x + 2 + x + 3\]
\[ = 2x + 5\]
\[ 2^{nd} \text{ method }:\]
\[\frac{d}{dx}\left[ \left( x + 2 \right)\left( x + 3 \right) \right] = \frac{d}{dx}\left( x^2 + 5x + 6 \right)\]
\[ = 2x + 5\]
\[\text{ Using both the methods, we get the same answer }.\]
APPEARS IN
RELATED QUESTIONS
Find the derivative of x–3 (5 + 3x).
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):
`(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):
`(ax + b)/(px^2 + qx + r)`
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):
(ax + b)n
Find the derivative of f (x) = 3x at x = 2
\[\frac{2}{x}\]
\[\frac{x^2 - 1}{x}\]
Differentiate of the following from first principle:
eax + b
Differentiate of the following from first principle:
− x
Differentiate of the following from first principle:
sin (2x − 3)
Differentiate each of the following from first principle:
\[\frac{\sin x}{x}\]
Differentiate each of the following from first principle:
\[3^{x^2}\]
tan (2x + 1)
\[\sqrt{\tan x}\]
\[\tan \sqrt{x}\]
\[\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)^3\]
2 sec x + 3 cot x − 4 tan x
\[\text{ If } y = \left( \sin\frac{x}{2} + \cos\frac{x}{2} \right)^2 , \text{ find } \frac{dy}{dx} at x = \frac{\pi}{6} .\]
x2 ex log x
xn tan x
\[\frac{2^x \cot x}{\sqrt{x}}\]
(1 − 2 tan x) (5 + 4 sin x)
sin2 x
(ax + b) (a + d)2
\[\frac{x^2 + 1}{x + 1}\]
\[\frac{x}{1 + \tan x}\]
\[\frac{x \sin x}{1 + \cos x}\]
\[\frac{{10}^x}{\sin x}\]
Write the derivative of f (x) = 3 |2 + x| at x = −3.
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 each of the following:
If\[f\left( x \right) = \frac{x^n - a^n}{x - a}\] then \[f'\left( a \right)\]
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.
Let f(x) = x – [x]; ∈ R, then f'`(1/2)` is ______.
