Advertisements
Advertisements
प्रश्न
Find `dy/dx if y = (sqrtx + 1/sqrtx)^2`
Advertisements
उत्तर
`y = (sqrtx + 1/sqrtx)^2`
∴ y = x + 2 + `1/x`
Differentiating w.r.t. x, we get
`dy/dx=d/dx(x + 2 + 1/x)`
= `d/dx(x) + d/dx (2) + d/dx(1/x)`
= `1+0+d/dx(x^(-1))`
= 1 + (–1) x–2
= `1 – 1/x^2`
APPEARS IN
संबंधित प्रश्न
Find the derivative of the following w. r. t.x. : `(3e^x-2)/(3e^x+2)`
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. : `1/("e"^x + 1)`
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 demand function is given as P = 175 + 9D + 25D2 . Find the revenue, average revenue, and marginal revenue when demand is 10.
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 followingfunctions.w.r.t.x.: `1/sqrtx`
Find `dy/dx if y=(sqrtx+1)^2`
Find `dy/dx if y = x^3 – 2x^2 + sqrtx + 1`
Find `dy/dx if y=(1+x)/(2+x)`
Find `dy/dx if y = ((logx+1))/x`
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.
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 = `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`
