Advertisements
Advertisements
प्रश्न
Find the derivative of the following w. r. t.x. : `(x^2+a^2)/(x^2-a^2)`
Advertisements
उत्तर
Let y = `(x^2 +"a"^2)/(x^2 - "a"^2)`
Differentiating w.r.t. x, we get
`dy/dx = d/dx((x^2 + "a"^2)/(x^2 - "a"^2))`
= `((x^2 - "a"^2)d/dx(x^2 + "a"^2) - (x^2 + "a"^2)d/dx(x^2 - "a"^2))/(x^2 - "a"^2)^2`
= `((x^2 - "a"^2)(d/dxx^2 + d/dx "a"^2)-(x^2 + "a"^2)(d/dxx^2 - d/dx "a"^2))/((x^2 - "a"^2)^2)`
= `((x^2 - "a"^2)(2x + 0) - (x^2 + "a"^2)(2x - 0))/((x^2 - "a"^2)^2)`
=`(2x(x^2 - "a"^2) - 2x(x^2 + "a"^2))/((x^2 - "a"^2)^2)`
= `(2x(x^2 - "a"^2 - x^2 - "a"^2))/((x^2 - "a"^2)^2)`
= `(2x(-2"a"^2))/((x^2 - "a"^2)^2)`
=`(-4x"a"^2)/((x^2 - "a"^2)^2)`
APPEARS IN
संबंधित प्रश्न
Differentiate the following function w.r.t.x : `(x^2 + 1)/x`
Differentiate the following function w.r.t.x. : `1/("e"^x + 1)`
Differentiate the following function w.r.t.x. : `"e"^x/("e"^x + 1)`
Differentiate the following function w.r.t.x. : `x/log x`
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: 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 following function w.r.t.x. : x−2
Differentiate the followingfunctions.w.r.t.x.: `1/sqrtx`
Find `dy/dx if y = x^2 + 1/x^2`
Find `dy/dx if y = (sqrtx + 1/sqrtx)^2`
Find `dy/dx if y = x^3 – 2x^2 + sqrtx + 1`
Find `dy/dx` if y = (1 – x) (2 – x)
Find `dy/dx if y = "e"^x/logx`
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.
