Advertisements
Advertisements
Question
Find the derivative of the following w. r. t.x.
`(3x^2 - 5)/(2x^3 - 4)`
Advertisements
Solution
Let y = `(3x^2 - 5)/(2x^3 - 4)`
using `dy/dx = (v(du)/dx - u(dv)/dx)/v^2`
let `(3x^2 - 5) = u and (2x^3 - 4) = v`
Differentiating w.r.t. x, we get
`dy/dx=d/dx((3x^2 - 5)/(2x^3 - 4))`
= `((2x^3 - 4)d/dx(3x^2 - 5) - (3x^2 - 5)d/dx(2x^3 - 4))/(2x^3 - 4)^2`
= `((2x^3 - 4)(3d/dxx^2 - d/dx5) - (3x^2 - 5)(2d/dxx^3 - d/dx4))/(2x^3 - 4)^2`
= `((2x^3 - 4)[3(2x - 0)] - (3x^2 - 5)[2(3x^2 - 0)])/(2x^3 - 4)^2`
= `((2x^3 - 4)[3(2x)] - (3x^2 - 5)[6x^2])/(2x^3 - 4)^2`
= `((2x^3 - 4)(6x) - (3x^2 - 5)(6x^2))/(2x^3 - 4)^2`
= `(6x(2x^3 - 4) - 6x^2(3x^2 - 5))/(2x^3 - 4)^2`
= `(12x^4 - 24x - 18x^4 + 30x^2)/(2x^3 - 4)^2`
= `(-6x^4 + 30x^2 - 24x)/(2x^3 - 4)^2`
APPEARS IN
RELATED QUESTIONS
Find the derivative of the following w. r. t.x. : `(x^2+a^2)/(x^2-a^2)`
Find the derivative of the following w. r. t. x. : `(xe^x)/(x+e^x)`
Differentiate the following function w.r.t.x : `(x^2 + 1)/x`
Differentiate the following function w.r.t.x. : `x/log x`
Differentiate the following function w.r.t.x. : `((2"e"^x - 1))/((2"e"^x + 1))`
Differentiate the following function w.r.t.x. : `((x+1)(x-1))/(("e"^x+1))`
The demand function of a commodity is given as P = 20 + D − D2. Find the rate at which price is changing when demand is 3.
Solve the following example: The total cost function of producing n notebooks is given by C= 1500 − 75n + 2n2 + `"n"^3/5`. Find the marginal cost at n = 10.
Solve the following example: The total cost of ‘t’ toy cars is given by C=5(2t)+17. Find the marginal cost and average cost at t = 3.
Solve the following example: If for a commodity; the demand function is given by, D = `sqrt(75 − 3"P")`. Find the marginal demand function when P = 5.
Solve the following example: The total cost of producing x units is given by C = 10e2x, find its marginal cost and average cost when x = 2.
Find `dy/dx if y = (sqrtx + 1/sqrtx)^2`
Find `dy/dx` if y = x2 + 2x – 1
Find `dy/dx`if y = x log x (x2 + 1)
The supply S of electric bulbs at price P is given by S = 2P3 + 5. Find the marginal supply when the price is ₹ 5/- Interpret the result.
If the total cost function is given by C = 5x3 + 2x2 + 1; Find the average cost and the marginal cost when x = 4.
Differentiate the following w.r.t.x :
y = `sqrt(x) + tan x - x^3`
Differentiate the following w.r.t.x :
y = `log x - "cosec" x + 5^x - 3/(x^(3/2))`
