Advertisements
Advertisements
Question
(ax + b)n (cx + d)n
Advertisements
Solution
\[\left( ax + b \right)^n \left( cx + d \right)^n \]
\[\text{ Let } u = \left( ax + b \right)^n , v = \left( cx + d \right)^n \]
\[\text{ Then }, u' = na \left( ax + b \right)^{n - 1} , v' = nc \left( cx + d \right)^{n - 1} \]
\[\text{ Using the product rule }: \]
\[\frac{d}{dx}\left( uv \right) = uv' + u'v\]
\[\frac{d}{dx}\left[ \left( ax + b \right)^n \left( cx + d \right)^n \right] = \left( ax + b \right)^n \times nc \left( cx + d \right)^{n - 1} + na \left( ax + b \right)^{n - 1} \times \left( cx + d \right)^n \]
\[ = n \left( ax + b \right)^{n - 1} \left( cx + d \right)^{n - 1} \left( acx + cb + acx + ad \right)\]
\[ = n \left( ax + b \right)^{n - 1} \left( cx + d \right)^{n - 1} \left( 2acx + cb + ad \right)\]
\[\]
APPEARS IN
RELATED QUESTIONS
Find the derivative of 99x at x = 100.
Find the derivative of `2x - 3/4`
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):
`(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):
`(1 + 1/x)/(1- 1/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):
`1/(ax^2 + bx + c)`
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):
`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):
`(a + bsin x)/(c + dcosx)`
Find the derivative of f (x) = tan x at x = 0
k xn
\[\frac{1}{\sqrt{3 - x}}\]
\[\sqrt{2 x^2 + 1}\]
Differentiate of the following from first principle:
(−x)−1
Differentiate of the following from first principle:
sin (x + 1)
Differentiate each of the following from first principle:
\[e^{x^2 + 1}\]
\[\left( x + \frac{1}{x} \right)\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)\]
\[\frac{2 x^2 + 3x + 4}{x}\]
\[\log\left( \frac{1}{\sqrt{x}} \right) + 5 x^a - 3 a^x + \sqrt[3]{x^2} + 6 \sqrt[4]{x^{- 3}}\]
cos (x + a)
\[\text{ If } y = \frac{2 x^9}{3} - \frac{5}{7} x^7 + 6 x^3 - x, \text{ find } \frac{dy}{dx} at x = 1 .\]
x2 ex log x
xn loga x
(x3 + x2 + 1) sin x
sin2 x
\[\frac{x^2 \cos\frac{\pi}{4}}{\sin x}\]
x−4 (3 − 4x−5)
\[\frac{e^x - \tan x}{\cot x - x^n}\]
\[\frac{\sin x - x \cos x}{x \sin x + \cos x}\]
\[\frac{a + \sin x}{1 + a \sin x}\]
\[\frac{3^x}{x + \tan x}\]
\[\frac{\sec x - 1}{\sec x + 1}\]
\[\frac{x + \cos x}{\tan x}\]
If x < 2, then write the value of \[\frac{d}{dx}(\sqrt{x^2 - 4x + 4)}\]
Write the value of \[\frac{d}{dx} \left\{ \left( x + \left| x \right| \right) \left| x \right| \right\}\]
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 each of the following:
If\[y = \frac{\sin x + \cos x}{\sin x - \cos x}\] then \[\frac{dy}{dx}\]at x = 0 is
Mark the correct alternative in each of the following:
If\[f\left( x \right) = \frac{x^n - a^n}{x - a}\] then \[f'\left( a \right)\]
