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):
`(px+ q) (r/s + s)`
Advertisements
उत्तर
Let f(x) = `(px + q) (r/x + s)` ...(i)
Differentiating (i) with respect to x, we get
∴ `d/(dx) (f(x))` = `(px + q). (r/x + s) + (px + q) (r/x + s)`
= `(p + 0) (r/x + s) + (px + q). ((xr' - rx')/(x^2) + 0)`
= `p(r/x + s) + (px + q) ((0 - r)/x^2)`
= `p(r/x + s) - ((px + q)r)/x^2`
= `(pr)/x + ps - (pr)/x - (qr)/x^2`
= `ps - (qr)/x^2`
APPEARS IN
संबंधित प्रश्न
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):
`(ax + b)/(cx + d)`
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):
`(sin(x + a))/ cos x`
Find the derivative of f (x) = 3x at x = 2
Find the derivative of f (x) = tan x at x = 0
Find the derivative of the following function at the indicated point:
2 cos x at x =\[\frac{\pi}{2}\]
\[\frac{x^2 + 1}{x}\]
(x + 2)3
Differentiate each of the following from first principle:
e−x
Differentiate of the following from first principle:
e3x
Differentiate of the following from first principle:
x cos x
Differentiate each of the following from first principle:
\[e^{x^2 + 1}\]
tan 2x
3x + x3 + 33
ex log a + ea long x + ea log a
\[\frac{2 x^2 + 3x + 4}{x}\]
\[\log\left( \frac{1}{\sqrt{x}} \right) + 5 x^a - 3 a^x + \sqrt[3]{x^2} + 6 \sqrt[4]{x^{- 3}}\]
Find the slope of the tangent to the curve f (x) = 2x6 + x4 − 1 at x = 1.
x3 sin x
x4 (5 sin x − 3 cos x)
x−3 (5 + 3x)
(ax + b) (a + d)2
\[\frac{2x - 1}{x^2 + 1}\]
\[\frac{x + e^x}{1 + \log x}\]
\[\frac{e^x - \tan x}{\cot x - x^n}\]
\[\frac{e^x + \sin x}{1 + \log x}\]
\[\frac{x \tan x}{\sec x + \tan x}\]
\[\frac{x \sin x}{1 + \cos x}\]
\[\frac{1 + 3^x}{1 - 3^x}\]
\[\frac{ax + b}{p x^2 + qx + r}\]
Write the value of \[\frac{d}{dx}\left( x \left| x \right| \right)\]
Mark the correct alternative in of the following:
If \[y = \frac{\sin\left( x + 9 \right)}{\cos x}\] then \[\frac{dy}{dx}\] at x = 0 is
Find the derivative of f(x) = tan(ax + b), by first principle.
