Advertisements
Advertisements
Question
Find `dy/dx if y = x^2 + 1/x^2`
Advertisements
Solution
`y = x^2 + 1/x^2`
∴ y = x2 + x–2
Differentiating w.r.t. x, we get
`dy/dx=d/dx(x^2+x^(-2))`
= `d/dx(x^2)+d/dx(x^-2)`
= 2x – 2x–3
= `2x – 2/x^3`
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. : `(3e^x-2)/(3e^x+2)`
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))`
If for a commodity; the price-demand relation is given as D =`("P"+ 5)/("P" - 1)`. Find the marginal demand when price is 2.
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: If the total cost function is given by; C = 5x3 + 2x2 + 7; find the average cost and the marginal cost when x = 4.
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: The total cost of producing x units is given by C = 10e2x, find its marginal cost and average cost when x = 2.
The cost of producing x articles is given by C = x2 + 15x + 81. Find the average cost and marginal cost functions. Find marginal cost when x = 10. Find x for which the marginal cost equals the average cost.
Differentiate the following function w.r.t.x. : `xsqrt x`
Find `dy/dx if y=(sqrtx+1)^2`
Find `dy/dx if y = "e"^x/logx`
Find `dy/dx`if y = x log x (x2 + 1)
The relation between price (P) and demand (D) of a cup of Tea is given by D = `12/"P"`. Find the rate at which the demand changes when the price is Rs. 2/-. Interpret the result.
