Advertisements
Advertisements
प्रश्न
Differentiate the following function w.r.t.x : `(x^2 + 1)/x`
Advertisements
उत्तर
Let y = `(x^2 + 1)/x`
Differentiating w.r.t. x, we get
`dy/dx= d/dx((x^2 + 1)/x)`
= `(xd/dx(x^2 + 1) - (x^2 + 1)d/dx(x))/x^2`
= `(x(2x + 0) - (x^2 + 1)(1))/x^2`
= `(2x^2 - x^2 - 1)/x^2`
`dy/dx=(x^2 - 1)/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. : `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 functions by the first principle: `1/(2x + 3)`
Differentiate the following function w.r.t.x. : `x/(x + 1)`
Differentiate the following function w.r.t.x. : `x/log x`
Differentiate the following function w.r.t.x. : `2^x/logx`
If for a commodity; the price-demand relation is given as D =`("P"+ 5)/("P" - 1)`. Find the marginal demand when price is 2.
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: 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.
Find `dy/dx if y = x^3 – 2x^2 + sqrtx + 1`
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 = `x^(4/3) + "e"^x - sinx`
Differentiate the following w.r.t.x :
y = `sqrt(x) + tan x - x^3`
Differentiate the following w.r.t.x :
y = `7^x + x^7 - 2/3 xsqrt(x) - logx + 7^7`
Select the correct answer from the given alternative:
If y = `(3x + 5)/(4x + 5)`, then `("d"y)/("d"x)` =
