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 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):
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):
cosec x cot 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):
`(sin(x + a))/ cos x`
\[\frac{x + 2}{3x + 5}\]
(x + 2)3
Differentiate of the following from first principle:
eax + b
Differentiate of the following from first principle:
x sin x
Differentiate each of the following from first principle:
\[\sqrt{\sin 2x}\]
Differentiate each of the following from first principle:
\[\sqrt{\sin (3x + 1)}\]
Differentiate each of the following from first principle:
\[e^\sqrt{2x}\]
Differentiate each of the following from first principle:
\[e^\sqrt{ax + b}\]
\[\sin \sqrt{2x}\]
\[\cos \sqrt{x}\]
x4 − 2 sin x + 3 cos x
3x + x3 + 33
\[\frac{2 x^2 + 3x + 4}{x}\]
a0 xn + a1 xn−1 + a2 xn−2 + ... + an−1 x + an.
\[\log\left( \frac{1}{\sqrt{x}} \right) + 5 x^a - 3 a^x + \sqrt[3]{x^2} + 6 \sqrt[4]{x^{- 3}}\]
\[If y = \sqrt{\frac{x}{a}} + \sqrt{\frac{a}{x}}, \text{ prove that } 2xy\frac{dy}{dx} = \left( \frac{x}{a} - \frac{a}{x} \right)\]
(x sin x + cos x) (x cos x − sin x)
\[e^x \log \sqrt{x} \tan x\]
x−3 (5 + 3x)
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)
(ax + b) (a + d)2
\[\frac{e^x}{1 + x^2}\]
\[\frac{x \tan x}{\sec x + \tan x}\]
\[\frac{x \sin x}{1 + \cos x}\]
\[\frac{4x + 5 \sin x}{3x + 7 \cos x}\]
\[\frac{x^5 - \cos x}{\sin x}\]
Write the value of \[\lim_{x \to a} \frac{x f (a) - a f (x)}{x - a}\]
Write the value of \[\frac{d}{dx}\left( x \left| x \right| \right)\]
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 of the following:
Let f(x) = x − [x], x ∈ R, then \[f'\left( \frac{1}{2} \right)\]
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 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 2x4 + x.
Find the derivative of x2 cosx.
Find the derivative of f(x) = tan(ax + b), by first principle.
