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.
`(3x^2 - 5)/(2x^3 - 4)`
Find the derivative of the following function by the first principle: 3x2 + 4
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)`
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: If for a commodity; the demand function is given by, D = `sqrt(75 − 3"P")`. Find the marginal demand function when P = 5.
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. : `xsqrt x`
Find `dy/dx if y = (sqrtx + 1/sqrtx)^2`
Find `dy/dx` if y = x2 + 2x – 1
Find `dy/dx` if y = (1 – x) (2 – x)
Find `dy/dx if y = ((logx+1))/x`
Find `dy/dx`if y = x log x (x2 + 1)
The demand (D) of biscuits at price P is given by D = `64/"P"^3`, find the marginal demand when price is Rs. 4/-.
Select the correct answer from the given alternative:
If y = `(x - 4)/(sqrtx + 2)`, then `("d"y)/("d"x)`
Select the correct answer from the given alternative:
If y = `(3x + 5)/(4x + 5)`, then `("d"y)/("d"x)` =
