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):
`a/x^4 = b/x^2 + cos x`
Advertisements
उत्तर
Let f(x) = `a/x^4 - b/x^2 + cos x`
= `d/dx (a/x^4) - d/dx (b/x^2) + d/dx (cos x)`
= `a d/dx (x^(-4)) - b d/dx (x^(-2)) + d/dx (cos x)`
= `a (-4x^(-5)) - b(-2 x^-3) + (-sin x)` `[d/dx (x^n) = nx^(n - 1) and d/dx (cos x) = -sin x]`
= `(-4a)/x^5 + (2b)/x^3 - sin x`
APPEARS IN
संबंधित प्रश्न
Find the derivative of (5x3 + 3x – 1) (x – 1).
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):
x4 (5 sin x – 3 cos x)
Find the derivative of f (x) = cos x at x = 0
Find the derivative of the following function at the indicated point:
k xn
(x2 + 1) (x − 5)
\[\sqrt{2 x^2 + 1}\]
Differentiate of the following from first principle:
sin (2x − 3)
Differentiate each of the following from first principle:
\[\sqrt{\sin 2x}\]
Differentiate each of the following from first principle:
\[\frac{\sin x}{x}\]
Differentiate each of the following from first principle:
\[\sqrt{\sin (3x + 1)}\]
Differentiate each of the following from first principle:
\[a^\sqrt{x}\]
x4 − 2 sin x + 3 cos x
\[\frac{x^3}{3} - 2\sqrt{x} + \frac{5}{x^2}\]
(2x2 + 1) (3x + 2)
\[\frac{2 x^2 + 3x + 4}{x}\]
cos (x + a)
Find the slope of the tangent to the curve f (x) = 2x6 + x4 − 1 at x = 1.
(x3 + x2 + 1) sin x
sin2 x
x3 ex cos x
\[\frac{x^2 \cos\frac{\pi}{4}}{\sin x}\]
x4 (5 sin x − 3 cos x)
(ax + b) (a + d)2
\[\frac{e^x - \tan x}{\cot x - x^n}\]
\[\frac{x}{1 + \tan x}\]
\[\frac{x \tan x}{\sec x + \tan x}\]
\[\frac{2^x \cot x}{\sqrt{x}}\]
\[\frac{1 + \log x}{1 - \log x}\]
Write the value of \[\lim_{x \to a} \frac{x f (a) - a f (x)}{x - a}\]
If f (x) = \[\frac{x^2}{\left| x \right|},\text{ write }\frac{d}{dx}\left( f (x) \right)\]
Write the value of \[\frac{d}{dx}\left( \log \left| x \right| \right)\]
If f (1) = 1, f' (1) = 2, then write the value of \[\lim_{x \to 1} \frac{\sqrt{f (x)} - 1}{\sqrt{x} - 1}\]
`(a + b sin x)/(c + d cos x)`
