Advertisements
Advertisements
प्रश्न
Differentiate the following function w.r.t.x. : `"e"^x/("e"^x + 1)`
Advertisements
उत्तर
y= `"e"^x/("e"^x + 1)`
Differentiating w.r.t. x, we get
`dy/dx = d/dx ("e"^x/("e"^x + 1))`
= `(("e"^x + 1)d/dx("e"^x) - "e"^"x" d/dx("e"^x + 1))/(("e"^x + 1)^2)`
= `(("e"^x + 1)"e"^x - "e"^x("e"^x + 0))/("e"^x + 1)^2`
= `("e"^x("e"^x + 1 - "e"^x))/("e"^x + 1)^2`
= `"e"^x/("e"^x + 1)^2`
APPEARS IN
संबंधित प्रश्न
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. : `1/("e"^x + 1)`
Differentiate the following function w.r.t.x. : `((x+1)(x-1))/(("e"^x+1))`
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.
The supply S for a commodity at price P is given by S = P2 + 9P − 2. Find the marginal supply when price is 7/-.
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. : x5
Differentiate the following function w.r.t.x. : x−2
Differentiate the followingfunctions.w.r.t.x.: `1/sqrtx`
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.
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 = `7^x + x^7 - 2/3 xsqrt(x) - logx + 7^7`
