Advertisements
Advertisements
Question
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)`
Advertisements
Solution
`d/dx((ax + b)/(px^2 + qr + r)) = ([d/dx(ax + b)](px^2 + qx + r) - (ax + b) d/dx(px^2 + qx + r))/(px^2 + qx + r)^2`
= `(a.(px^2 + qx + r) - (ax + b). (2px +q))/(px^2 + qx + r)^2`
= `((apx^2 + aqx + ar) - [2apx^2 + (aq + 2bp)x + bq])/((px^2 + qx + r)^2)`
= `(-apx^2 + ar - 2bpx - bq)/((px^2 + qx + r)^2)`
= `(-apx^2 - 2bpx + ar - bq)/((px^2 + qx + r)^2)`
APPEARS IN
RELATED QUESTIONS
Find the derivative of x2 – 2 at x = 10.
Find the derivative of x at x = 1.
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 `2x - 3/4`
Find the derivative of x–3 (5 + 3x).
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):
(ax + b)n (cx + d)m
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 =\[\frac{\pi}{2}\]
\[\frac{1}{x^3}\]
Differentiate of the following from first principle:
e3x
Differentiate of the following from first principle:
− x
Differentiate of the following from first principle:
(−x)−1
Differentiate each of the following from first principle:
\[\sqrt{\sin (3x + 1)}\]
3x + x3 + 33
(2x2 + 1) (3x + 2)
\[\frac{a \cos x + b \sin x + c}{\sin x}\]
\[\text{ If } y = \left( \frac{2 - 3 \cos x}{\sin x} \right), \text{ find } \frac{dy}{dx} at x = \frac{\pi}{4}\]
Find the slope of the tangent to the curve f (x) = 2x6 + x4 − 1 at x = 1.
\[If y = \sqrt{\frac{x}{a}} + \sqrt{\frac{a}{x}}, \text{ prove that } 2xy\frac{dy}{dx} = \left( \frac{x}{a} - \frac{a}{x} \right)\]
x3 sin x
x3 ex
xn tan x
\[\frac{2^x \cot x}{\sqrt{x}}\]
x5 ex + x6 log x
(x sin x + cos x) (x cos x − sin x)
\[\frac{x^2 \cos\frac{\pi}{4}}{\sin x}\]
\[\frac{x^2 + 1}{x + 1}\]
\[\frac{e^x - \tan x}{\cot x - x^n}\]
\[\frac{x \tan x}{\sec x + \tan x}\]
\[\frac{\sqrt{a} + \sqrt{x}}{\sqrt{a} - \sqrt{x}}\]
If f (x) = \[\log_{x_2}\]write the value of f' (x).
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.
Find the derivative of f(x) = tan(ax + b), by first principle.
