Advertisements
Advertisements
प्रश्न
Find the derivative of the following w. r. t.x. : `(3e^x-2)/(3e^x+2)`
Advertisements
उत्तर
Let y = `(3"e"^x - 2)/(3"e"^x + 2)`
Differentiating w.r.t. x, we get
`dy/dx = d/dx((3"e"^x - 2)/(3"e"^x + 2))`
=`((3"e"^x + 2) d/dx(3"e"^x - 2) - (3"e"^x - 2) d/dx(3"e"^x + 2))/((3"e"^x + 2)^2)`
= `((3"e"^x + 2)(d/dx(3"e"^x) - d/dx(2)) - (3"e"^x - 2)(d/dx(3"e"^x) + d/dx(2)))/((3"e"^x + 2)^2)`
= `((3"e"^x + 2)(3"e"^x - 0) - (3"e"^x - 2)(3"e"^x + 0))/((3"e"^x + 2)^2)`
= `(3"e"^x(3"e"^x + 2) - 3"e"^x(3"e"^x - 2))/((3"e"^x + 2)^2)`
= `(3"e"^x(3"e"^x + 2 - 3"e"^x + 2))/(3"e"^x + 2)^2`
= `(3"e"^x(4))/(3"e"^x + 2)^2`
= `(12"e"^x)/(3"e"^x + 2)^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. : `logx/(x^3-5)`
Find the derivative of the following w. r. t. x. : `(xe^x)/(x+e^x)`
Find the derivative of the following function by the first principle: 3x2 + 4
Differentiate the following function w.r.t.x : `(x^2 + 1)/x`
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))`
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 function of producing n notebooks is given by C= 1500 − 75n + 2n2 + `"n"^3/5`. Find the marginal cost at n = 10.
Differentiate the following function .w.r.t.x. : x5
Differentiate the following function w.r.t.x. : `xsqrt x`
Find `dy/dx` if y = x2 + 2x – 1
Find `dy/dx` if y = (1 – x) (2 – x)
Find `dy/dx if y=(1+x)/(2+x)`
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.
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 = `log x - "cosec" x + 5^x - 3/(x^(3/2))`
Differentiate the following w.r.t.x :
y = `3 cotx - 5"e"^x + 3logx - 4/(x^(3/4))`
Select the correct answer from the given alternative:
If y = `(3x + 5)/(4x + 5)`, then `("d"y)/("d"x)` =
