Advertisements
Advertisements
प्रश्न
x3 sin x
Advertisements
उत्तर
\[\text{ Let } u = x^3 ; v = \sin x\]
\[\text{ Then }, u' = 3 x^2 ; v' = \cos x\]
\[\text{ Using the product rule }:\]
\[\frac{d}{dx}\left( uv \right) = uv' + vu'\]
\[\frac{d}{dx}\left( x^3 \sin x \right) = x^3 \cos x + \sin x \left( 3 x^2 \right)\]
\[ = x^2 \left( x \cos x + 3 \sin x \right)\]
APPEARS IN
संबंधित प्रश्न
Find the derivative of 99x at x = 100.
Find the derivative of `2x - 3/4`
Find the derivative of (5x3 + 3x – 1) (x – 1).
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):
`(1 + 1/x)/(1- 1/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):
`1/(ax^2 + bx + c)`
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):
`4sqrtx - 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):
`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):
`(sec x - 1)/(sec x + 1)`
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`
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) = x2 − 2 at x = 10
Find the derivative of f (x) = cos x at x = 0
Find the derivative of the following function at the indicated point:
Find the derivative of the following function at the indicated point:
sin 2x at x =\[\frac{\pi}{2}\]
Differentiate each of the following from first principle:
e−x
Differentiate each of the following from first principle:
\[\sqrt{\sin 2x}\]
tan2 x
tan (2x + 1)
\[\tan \sqrt{x}\]
x4 − 2 sin x + 3 cos x
ex log a + ea long x + ea log a
\[\frac{a \cos x + b \sin x + c}{\sin x}\]
\[\text{ If } y = \left( \sin\frac{x}{2} + \cos\frac{x}{2} \right)^2 , \text{ find } \frac{dy}{dx} at x = \frac{\pi}{6} .\]
Find the rate at which the function f (x) = x4 − 2x3 + 3x2 + x + 5 changes with respect to x.
If for f (x) = λ x2 + μ x + 12, f' (4) = 15 and f' (2) = 11, then find λ and μ.
(x sin x + cos x) (x cos x − sin x)
(1 +x2) cos x
x3 ex cos x
x−3 (5 + 3x)
(ax + b) (a + d)2
\[\frac{1 + 3^x}{1 - 3^x}\]
\[\frac{a + b \sin x}{c + d \cos x}\]
\[\frac{x^5 - \cos x}{\sin x}\]
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 x2 cosx.
