Advertisements
Advertisements
प्रश्न
(ax + b)n (cx + d)n
Advertisements
उत्तर
\[\left( ax + b \right)^n \left( cx + d \right)^n \]
\[\text{ Let } u = \left( ax + b \right)^n , v = \left( cx + d \right)^n \]
\[\text{ Then }, u' = na \left( ax + b \right)^{n - 1} , v' = nc \left( cx + d \right)^{n - 1} \]
\[\text{ Using the product rule }: \]
\[\frac{d}{dx}\left( uv \right) = uv' + u'v\]
\[\frac{d}{dx}\left[ \left( ax + b \right)^n \left( cx + d \right)^n \right] = \left( ax + b \right)^n \times nc \left( cx + d \right)^{n - 1} + na \left( ax + b \right)^{n - 1} \times \left( cx + d \right)^n \]
\[ = n \left( ax + b \right)^{n - 1} \left( cx + d \right)^{n - 1} \left( acx + cb + acx + ad \right)\]
\[ = n \left( ax + b \right)^{n - 1} \left( cx + d \right)^{n - 1} \left( 2acx + cb + ad \right)\]
\[\]
APPEARS IN
संबंधित प्रश्न
Find the derivative of x2 – 2 at x = 10.
Find the derivative of x5 (3 – 6x–9).
Find the derivative of x–4 (3 – 4x–5).
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):
`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):
`(a + bsin x)/(c + dcosx)`
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):
x4 (5 sin x – 3 cos x)
Find the derivative of f (x) = 3x at x = 2
Find the derivative of the following function at the indicated point:
sin x at x =\[\frac{\pi}{2}\]
\[\frac{x + 1}{x + 2}\]
\[\frac{1}{\sqrt{3 - x}}\]
Differentiate of the following from first principle:
e3x
Differentiate of the following from first principle:
sin (x + 1)
Differentiate each of the following from first principle:
x2 sin x
Differentiate each of the following from first principle:
\[e^\sqrt{ax + b}\]
tan2 x
tan (2x + 1)
\[\sin \sqrt{2x}\]
\[\tan \sqrt{x}\]
\[\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)^3\]
cos (x + a)
Find the slope of the tangent to the curve f (x) = 2x6 + x4 − 1 at x = 1.
If for f (x) = λ x2 + μ x + 12, f' (4) = 15 and f' (2) = 11, then find λ and μ.
xn tan x
x2 sin x log x
x5 ex + x6 log 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.
(3 sec x − 4 cosec x) (−2 sin x + 5 cos x)
\[\frac{x \sin x}{1 + \cos x}\]
\[\frac{\sqrt{a} + \sqrt{x}}{\sqrt{a} - \sqrt{x}}\]
\[\frac{{10}^x}{\sin x}\]
\[\frac{4x + 5 \sin x}{3x + 7 \cos x}\]
\[\frac{x}{1 + \tan x}\]
\[\frac{1}{a x^2 + bx + c}\]
Write the value of the derivative of f (x) = |x − 1| + |x − 3| at x = 2.
Write the value of \[\frac{d}{dx}\left( \log \left| x \right| \right)\]
Mark the correct alternative in each of the following:
If\[f\left( x \right) = \frac{x^n - a^n}{x - a}\] then \[f'\left( a \right)\]
Find the derivative of f(x) = tan(ax + b), by first principle.
(ax2 + cot x)(p + q cos x)
