Advertisements
Advertisements
प्रश्न
x4 (5 sin x − 3 cos x)
उत्तर
\[\text{ Let } u = x^4 ; v = 5 \sin x - 3 \cos x\]
\[\text{ Then }, u' = 4 x^3 ; v' = 5 \cos x - 3 ( - \sin x) = 5 \cos x + 3 \sin x \]
\[\text{ According to the product rule }:\]
\[\frac{d}{dx}\left( uv \right) = u v' + v u'\]
\[\frac{d}{dx}\left( x^4 \left( 5 \sin x - 3 \cos x \right) \right) = x^4 \left( 5 \cos x + 3 \sin x \right) + \left( 5 \sin x - 3 \cos x \right) 4 x^3 \]
\[ = x^3 \left( 5x \cos x + 3 x \sin x + 20 \sin x - 12 \cos x \right)\]
\[ = x^3 \left( \left( 3x + 20 \right) \sin x + \left( 5x - 12 \right) \cos x \right)\]
\[ = 3 x^4 \sin x + 20 x^3 \sin x + 5x \cos x - 12 \cos x\]
APPEARS IN
संबंधित प्रश्न
Find the derivative of x at 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):
`(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)/(px^2 + qx + r)`
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):
`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):
sinn 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):
x4 (5 sin x – 3 cos x)
Find the derivative of f (x) = 3x at x = 2
Find the derivative of f (x) = 99x at x = 100
\[\frac{x^2 + 1}{x}\]
\[\frac{2x + 3}{x - 2}\]
Differentiate of the following from first principle:
eax + b
x ex
Differentiate of the following from first principle:
− x
Differentiate each of the following from first principle:
\[\sqrt{\sin (3x + 1)}\]
Differentiate each of the following from first principle:
\[a^\sqrt{x}\]
Differentiate each of the following from first principle:
\[3^{x^2}\]
tan2 x
tan 2x
\[\frac{1}{\sin x} + 2^{x + 3} + \frac{4}{\log_x 3}\]
\[\frac{(x + 5)(2 x^2 - 1)}{x}\]
\[\log\left( \frac{1}{\sqrt{x}} \right) + 5 x^a - 3 a^x + \sqrt[3]{x^2} + 6 \sqrt[4]{x^{- 3}}\]
x3 sin x
x2 ex log x
x5 (3 − 6x−9)
(ax + b)n (cx + d)n
\[\frac{x^2 + 1}{x + 1}\]
\[\frac{e^x - \tan x}{\cot x - x^n}\]
\[\frac{x}{1 + \tan x}\]
\[\frac{x \tan x}{\sec x + \tan x}\]
\[\frac{4x + 5 \sin x}{3x + 7 \cos x}\]
Write the value of \[\lim_{x \to a} \frac{x f (a) - a f (x)}{x - a}\]
If |x| < 1 and y = 1 + x + x2 + x3 + ..., then write the value of \[\frac{dy}{dx}\]
If f (x) = \[\log_{x_2}\]write the value of f' (x).
Mark the correct alternative in of the following:
If\[f\left( x \right) = 1 - x + x^2 - x^3 + . . . - x^{99} + x^{100}\]then \[f'\left( 1 \right)\]
