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 function by the first principle: 3x2 + 4
Differentiate the following function w.r.t.x. : `1/("e"^x + 1)`
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.
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 producing x units is given by C = 10e2x, find its marginal cost and average cost when x = 2.
Differentiate the following function .w.r.t.x. : x5
Differentiate the following function w.r.t.x. : x−2
Find `dy/dx if y=(sqrtx+1)^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/-.
Differentiate the following w.r.t.x :
y = `x^(4/3) + "e"^x - sinx`
Differentiate the following w.r.t.x :
y = `sqrt(x) + tan x - x^3`
Differentiate the following w.r.t.x :
y = `x^(7/3) + 5x^(4/5) - 5/(x^(2/5))`
Differentiate the following w.r.t.x :
y = `3 cotx - 5"e"^x + 3logx - 4/(x^(3/4))`
