Advertisements
Advertisements
Question
Differentiate the following function w.r.t.x : `(x^2 + 1)/x`
Advertisements
Solution
Let y = `(x^2 + 1)/x`
Differentiating w.r.t. x, we get
`dy/dx= d/dx((x^2 + 1)/x)`
= `(xd/dx(x^2 + 1) - (x^2 + 1)d/dx(x))/x^2`
= `(x(2x + 0) - (x^2 + 1)(1))/x^2`
= `(2x^2 - x^2 - 1)/x^2`
`dy/dx=(x^2 - 1)/x^2`
APPEARS IN
RELATED QUESTIONS
Find the derivative of the following w. r. t.x.
`(3x^2 - 5)/(2x^3 - 4)`
Find the derivative of the following w. r. t. x. : `logx/(x^3-5)`
Find the derivative of the following w. r. t.x. : `(3e^x-2)/(3e^x+2)`
Find the derivative of the following function by the first principle: `x sqrtx`
Differentiate the following function w.r.t.x. : `"e"^x/("e"^x + 1)`
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.
The supply S for a commodity at price P is given by S = P2 + 9P − 2. Find the marginal supply when price is 7/-.
Differentiate the followingfunctions.w.r.t.x.: `1/sqrtx`
Find `dy/dx if y = x^2 + 1/x^2`
Find `dy/dx` if y = (1 – x) (2 – x)
Find `dy/dx if y = ((logx+1))/x`
Find `dy/dx`if y = x log x (x2 + 1)
The demand (D) of biscuits at price P is given by D = `64/"P"^3`, find the marginal demand when price is Rs. 4/-.
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 = `x^(7/3) + 5x^(4/5) - 5/(x^(2/5))`
Select the correct answer from the given alternative:
If y = `(3x + 5)/(4x + 5)`, then `("d"y)/("d"x)` =
