Advertisements
Advertisements
प्रश्न
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`
Advertisements
उत्तर
`d/dx 4sqrtx - 2 = d/dx (4x^(1/2) - 2)`
= `4 xx 1/2 x^(1/2 - 1) - 0`
= `2/sqrtx`
APPEARS IN
संबंधित प्रश्न
For the function
f(x) = `x^100/100 + x^99/99 + ...+ x^2/2 + x + 1`
Prove that f'(1) = 100 f'(0)
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):
`(sec x - 1)/(sec x + 1)`
Find the derivative of f (x) = 3x at x = 2
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:
2 cos x at x =\[\frac{\pi}{2}\]
Find the derivative of the following function at the indicated point:
sin 2x at x =\[\frac{\pi}{2}\]
\[\frac{2}{x}\]
x ex
Differentiate each of the following from first principle:
\[\frac{\cos x}{x}\]
Differentiate each of the following from first principle:
sin x + cos x
tan2 x
x4 − 2 sin x + 3 cos x
\[\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)^3\]
\[\frac{(x + 5)(2 x^2 - 1)}{x}\]
Find the slope of the tangent to the curve f (x) = 2x6 + x4 − 1 at x = 1.
sin x cos x
x−4 (3 − 4x−5)
x−3 (5 + 3x)
Differentiate in two ways, using product rule and otherwise, the function (1 + 2 tan x) (5 + 4 cos x). Verify that the answers are the same.
\[\frac{x^2 + 1}{x + 1}\]
\[\frac{1}{a x^2 + bx + c}\]
\[\frac{e^x}{1 + x^2}\]
\[\frac{x \sin x}{1 + \cos x}\]
\[\frac{\sqrt{a} + \sqrt{x}}{\sqrt{a} - \sqrt{x}}\]
\[\frac{{10}^x}{\sin x}\]
\[\frac{x}{1 + \tan x}\]
\[\frac{x^5 - \cos x}{\sin x}\]
If \[\frac{\pi}{2}\] then find \[\frac{d}{dx}\left( \sqrt{\frac{1 + \cos 2x}{2}} \right)\]
Write the derivative of f (x) = 3 |2 + x| at x = −3.
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 \[f\left( x \right) = \frac{x - 4}{2\sqrt{x}}\]
