Advertisements
Advertisements
प्रश्न
Find the derivative of the following w. r. t. x. : `(xe^x)/(x+e^x)`
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 function by the first principle: `x sqrtx`
Differentiate the following function w.r.t.x. : `x/(x + 1)`
Differentiate the following function w.r.t.x. : `1/("e"^x + 1)`
Differentiate the following function w.r.t.x. : `2^x/logx`
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.
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 following function w.r.t.x. : `xsqrt x`
Find `dy/dx` if y = x2 + 2x – 1
Find `dy/dx if y = "e"^x/logx`
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 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.
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 = `7^x + x^7 - 2/3 xsqrt(x) - logx + 7^7`
