Advertisements
Advertisements
प्रश्न
Find the derivative of the following w. r. t. x. : `(xe^x)/(x+e^x)`
Advertisements
उत्तर
Let y = `(x"e"^x)/(x + "e"^x)`
Differentiating w.r.t. x, we get
`dy/dx = d/dx((x"e"^x)/(x + "e"^x))`
= `((x + "e"^x)d/dx(x"e"^x) -(x"e"^x)d/dx(x + "e"^x))/(x + "e"^x)^2`
=`((x + "e"^x)[xd/dx("e"^x) + "e"^xd/dx(x)] - x"e"^x(d/dx(x) + d/dx("e"^x)))/(x + "e"^x)^2`
= `((x + "e"^x)[x"e"^x + "e"^x(1)] - x"e"^x(1 + "e"^x))/(x + "e"^x)^2`
=`((x + "e"^x)(x"e"^x + "e"^x) - x"e"^x(1 + "e"^x))/(x + "e"^x)^2`
= `((x + "e"^x)"e"^x(x + 1) - x"e"^x(1 + "e"^x))/(x + "e"^x)^2`
= `("e"^x[(x + "e"^x)(x + 1) - x(1 + "e"^x)])/(x + "e"^x)^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. : `(3e^x-2)/(3e^x+2)`
Find the derivative of the following function by the first principle: 3x2 + 4
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. : `x/log x`
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.
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. : x−2
Differentiate the following function w.r.t.x. : `xsqrt x`
Find `dy/dx` if y = x2 + 2x – 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/-.
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 = `7^x + x^7 - 2/3 xsqrt(x) - logx + 7^7`
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 = `(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)` =
