Advertisements
Advertisements
प्रश्न
Differentiate the following function w.r.t.x. : `1/("e"^x + 1)`
Advertisements
उत्तर
Let y = `1/(e^x + 1)`
Differentiating w.r.t. x, we get
`"dy"/"dx" = "d"/"dx" (1/("e"^x+1))`
= `(("e"^x + 1)d/dx(1) - (1)d/dx("e"^x + 1))/(("e"^x + 1)^2`
= `(("e"^x + 1)(0) - (1)("e"^x + 0))/(("e"^x + 1)^2`
= `(0 - "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.
`(3x^2 - 5)/(2x^3 - 4)`
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/(x + 1)`
Differentiate the following function w.r.t.x : `(x^2 + 1)/x`
Differentiate the following function w.r.t.x. : `"e"^x/("e"^x + 1)`
Differentiate the following function w.r.t.x. : `((2"e"^x - 1))/((2"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: 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 of ‘t’ toy cars is given by C=5(2t)+17. Find the marginal cost and average cost at t = 3.
Differentiate the following function w.r.t.x. : `xsqrt x`
Differentiate the followingfunctions.w.r.t.x.: `1/sqrtx`
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 = x2 + 2x – 1
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.
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.
Select the correct answer from the given alternative:
If y = `(3x + 5)/(4x + 5)`, then `("d"y)/("d"x)` =
