Advertisements
Advertisements
प्रश्न
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
Advertisements
उत्तर
Let f(x) = (ax + b)(cx + d)2
By Leibnitz product rule,
∴ `f'(x) = (ax + b) d/dx (cx + d)^2 + (cx + d)^2 d/dx (ax + d)`
= `(ax + b) d/dx (c^2 x^2 + 2cdx + d^2) + (cx + d)^2 d/dx (ax + b)`
= `(ax + b)[d/dx (c^2x^2) + d/dx (2cdx) + d/dx d^2] + (cx + d)^2 [d/dx ax + d/dx b]`
= (ax + b)(2c2x + 2cd) + (cx + d2)a
= 2c(ax + b) (cx + d) + a(cx + d)2
APPEARS IN
संबंधित प्रश्न
Find the derivative of x2 – 2 at x = 10.
Find the derivative of 99x at x = 100.
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`
\[\frac{x + 1}{x + 2}\]
Differentiate each of the following from first principle:
e−x
Differentiate of the following from first principle:
e3x
x ex
Differentiate of the following from first principle:
\[\cos\left( x - \frac{\pi}{8} \right)\]
Differentiate each of the following from first principle:
\[e^\sqrt{ax + b}\]
Differentiate each of the following from first principle:
\[a^\sqrt{x}\]
\[\cos \sqrt{x}\]
\[\tan \sqrt{x}\]
x4 − 2 sin x + 3 cos x
3x + x3 + 33
\[\frac{a \cos x + b \sin x + c}{\sin x}\]
cos (x + a)
\[\text{ If } y = \frac{2 x^9}{3} - \frac{5}{7} x^7 + 6 x^3 - x, \text{ find } \frac{dy}{dx} at x = 1 .\]
sin2 x
x3 ex cos x
x4 (5 sin x − 3 cos x)
x−4 (3 − 4x−5)
(ax + b)n (cx + d)n
\[\frac{x + e^x}{1 + \log x}\]
\[\frac{x}{1 + \tan x}\]
\[\frac{e^x}{1 + x^2}\]
\[\frac{2^x \cot x}{\sqrt{x}}\]
\[\frac{{10}^x}{\sin x}\]
\[\frac{1 + 3^x}{1 - 3^x}\]
\[\frac{p x^2 + qx + r}{ax + b}\]
\[\frac{x}{\sin^n x}\]
\[\frac{1}{a x^2 + bx + c}\]
If f (x) = \[\frac{x^2}{\left| x \right|},\text{ write }\frac{d}{dx}\left( f (x) \right)\]
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 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 of the following:
If \[y = \frac{\sin\left( x + 9 \right)}{\cos x}\] then \[\frac{dy}{dx}\] at x = 0 is
Find the derivative of f(x) = tan(ax + b), by first principle.
(ax2 + cot x)(p + q cos x)
`(a + b sin x)/(c + d cos x)`
