Advertisements
Advertisements
प्रश्न
Find the derivative of x5 (3 – 6x–9).
Advertisements
उत्तर
Let f (x) = x5 (3 – 6x–9)
By Leibnitz product rule,
f'(x) = `x^5 d/(dx) (3 - 6x^-9) + (3 - 6x^-9) d/(dx) (x^5)`
= x5 {0 - 6(-9)x-9-1} + (3 - 6x-9)(5x4)
= x5 (54x-10) + 15x4 - 30x-5
= 54x-5 + 15x4 - 30x-5
= 24x-5 + 15x4
= `15x^4 + 24/x^5`
APPEARS IN
संबंधित प्रश्न
Find the derivative of (5x3 + 3x – 1) (x – 1).
Find the derivative of x–3 (5 + 3x).
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):
(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):
`(sec x - 1)/(sec x + 1)`
Find the derivative of f (x) = 3x at x = 2
\[\frac{2}{x}\]
\[\frac{x^2 - 1}{x}\]
(x + 2)3
\[\sqrt{2 x^2 + 1}\]
Differentiate of the following from first principle:
eax + b
x ex
Differentiate of the following from first principle:
sin (x + 1)
Differentiate each of the following from first principle:
\[e^\sqrt{ax + b}\]
\[\tan \sqrt{x}\]
ex log a + ea long x + ea log a
(2x2 + 1) (3x + 2)
log3 x + 3 loge x + 2 tan x
\[\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)^3\]
\[\text{ If } y = \left( \sin\frac{x}{2} + \cos\frac{x}{2} \right)^2 , \text{ find } \frac{dy}{dx} at x = \frac{\pi}{6} .\]
xn tan x
(1 − 2 tan x) (5 + 4 sin x)
(1 +x2) cos x
sin2 x
x3 ex cos 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.
(3x2 + 2)2
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)
\[\frac{x^2 + 1}{x + 1}\]
\[\frac{\sqrt{a} + \sqrt{x}}{\sqrt{a} - \sqrt{x}}\]
\[\frac{4x + 5 \sin x}{3x + 7 \cos x}\]
\[\frac{\sec x - 1}{\sec x + 1}\]
Write the value of \[\frac{d}{dx} \left\{ \left( x + \left| x \right| \right) \left| x \right| \right\}\]
If f (x) = |x| + |x−1|, write the value of \[\frac{d}{dx}\left( f (x) \right)\]
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\[y = 1 + \frac{x}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + . . .\]then \[\frac{dy}{dx} =\]
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
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.
