Advertisements
Advertisements
प्रश्न
x2 sin x log x
Advertisements
उत्तर
\[\text{ Let } u = x^2 ; v = \sin x; w = \log x\]
\[\text{ Then }, u' = 2x; v' = \cos x; w' = \frac{1}{x}\]
\[\text{ Using the product rule }:\]
\[\frac{d}{dx}\left( uvw \right) = u'vw + uv'w + uvw'\]
\[\frac{d}{dx}\left( x^2 \sin x \log x \right) = 2x \sin x \log x + x^2 \cos x \log x + x^2 \sin x . \frac{1}{x}\]
\[ = 2x \sin x \log x + x^2 \cos x \log x + x \sin x\]
APPEARS IN
संबंधित प्रश्न
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):
`(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):
`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):
(ax + b)n (cx + d)m
Find the derivative of the following function at the indicated point:
sin x at x =\[\frac{\pi}{2}\]
\[\frac{x^2 + 1}{x}\]
k xn
(x + 2)3
Differentiate each of the following from first principle:
e−x
Differentiate of the following from first principle:
e3x
Differentiate each of the following from first principle:
x2 ex
Differentiate each of the following from first principle:
\[e^\sqrt{2x}\]
Differentiate each of the following from first principle:
\[e^\sqrt{ax + b}\]
ex log a + ea long x + ea log a
\[\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)^3\]
\[\frac{( x^3 + 1)(x - 2)}{x^2}\]
Find the slope of the tangent to the curve f (x) = 2x6 + x4 − 1 at x = 1.
x2 ex log x
(x sin x + cos x) (x cos x − sin x)
\[e^x \log \sqrt{x} \tan x\]
x3 ex cos x
(ax + b) (a + d)2
\[\frac{x + e^x}{1 + \log x}\]
\[\frac{1}{a x^2 + bx + c}\]
\[\frac{x^2 - x + 1}{x^2 + x + 1}\]
\[\frac{{10}^x}{\sin x}\]
\[\frac{1 + \log x}{1 - \log x}\]
Write the value of \[\lim_{x \to c} \frac{f(x) - f(c)}{x - c}\]
Write the value of \[\lim_{x \to a} \frac{x f (a) - a f (x)}{x - a}\]
If \[\frac{\pi}{2}\] then find \[\frac{d}{dx}\left( \sqrt{\frac{1 + \cos 2x}{2}} \right)\]
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:
If \[f\left( x \right) = \frac{x - 4}{2\sqrt{x}}\]
Mark the correct alternative in of the following:
If\[f\left( x \right) = 1 - x + x^2 - x^3 + . . . - x^{99} + x^{100}\]then \[f'\left( 1 \right)\]
Mark the correct alternative in of the following:
If \[f\left( x \right) = x^{100} + x^{99} + . . . + x + 1\] then \[f'\left( 1 \right)\] is equal to
Find the derivative of 2x4 + x.
Find the derivative of f(x) = tan(ax + b), by first principle.
