Advertisements
Advertisements
Question
Find `dy/dx if y=(1+x)/(2+x)`
Solution
`y=(1+x)/(2+x)`
Differentiating w.r.t. x, we get
`dy/dx = d/dx ((1+x)/(2+x))`
=`((2 + x)d/dx(1 + x) - (1 + x)d/dx(2 + x))/(2 + x)^2`
=`((2 + x)(0 + 1) - (1 + x)(0 + 1))/(2 + x)^2`
`dy/dx = ((2 + x) - (1 + x))/(2 + x)^2`
=`(2 + x - 1 - x)/(2 + x)^2`
=`1/(2 + x)^2`
APPEARS IN
RELATED QUESTIONS
Find the derivative of the following w. r. t.x. : `(x^2+a^2)/(x^2-a^2)`
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 : `(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`
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.
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 demand function is given as P = 175 + 9D + 25D2 . Find the revenue, average revenue, and marginal revenue when demand is 10.
Differentiate the following function w.r.t.x. : `xsqrt x`
Find `dy/dx if y = x^2 + 1/x^2`
Find `dy/dx if y = "e"^x/logx`
Differentiate the following w.r.t.x :
y = `x^(4/3) + "e"^x - sinx`
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)` =
