Advertisements
Advertisements
प्रश्न
Differentiate the following function w.r.t.x. : `((x+1)(x-1))/(("e"^x+1))`
Advertisements
उत्तर
Let y = `((x + 1)(x - 1))/(("e"^x + 1))`
∴ y = `(x^2 - 1)/(("e"^x + 1))`
Differentiating w.r.t. x, we get
`dy/dx=d/dx((x^2 - 1)/("e"^x + 1))`
= `(("e"^x + 1)d/dx(x^2 - 1) - (x^2 - 1)d/dx("e"^x + 1))/("e"^x + 1)^2`
= `(("e"^x + 1)(2x) - (x^2 - 1)("e"^x + 0))/("e"^x + 1)^2`
= `(2x"e"^x + 2x - x^2"e"^x + "e"^x)/("e"^x + 1)^2`
= `(2x"e"^x + "e"^x - x^2"e"^x + 2x)/("e"^x + 1)^2`
= `("e"^x(2x + 1 - x^2) + 2x)/("e"^x + 1)^2`
APPEARS IN
संबंधित प्रश्न
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.
`(3x^2 - 5)/(2x^3 - 4)`
Find the derivative of the following w. r. t.x. : `(3e^x-2)/(3e^x+2)`
Find the derivative of the following w. r. t. x. : `(xe^x)/(x+e^x)`
Differentiate the following function w.r.t.x. : `2^x/logx`
If for a commodity; the price-demand relation is given as D =`("P"+ 5)/("P" - 1)`. Find the marginal demand when price is 2.
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.
Solve the following example: The demand function is given as P = 175 + 9D + 25D2 . Find the revenue, average revenue, and marginal revenue when demand is 10.
Find `dy/dx if y = x^2 + 1/x^2`
Find `dy/dx if y = (sqrtx + 1/sqrtx)^2`
Find `dy/dx` if y = (1 – x) (2 – x)
Find `dy/dx if y=(1+x)/(2+x)`
Find `dy/dx if y = "e"^x/logx`
Find `dy/dx`if y = x log x (x2 + 1)
If the total cost function is given by C = 5x3 + 2x2 + 1; Find the average cost and the marginal cost when x = 4.
