English

Differentiate the followingfunctions.w.r.t.x. : 1x - Mathematics and Statistics

Advertisements
Advertisements

Question

Differentiate the followingfunctions.w.r.t.x.: `1/sqrtx`

Sum

Solution

Let y =`1/sqrtx`

∴ `y =x^((-1)/2)`

Differentiating w.r.t. x, we get

`dy/dx=(-1)/2x^((-3)/2)`

= `(-1)/(2x^(3/2))`

shaalaa.com
Rules of Differentiation (Without Proof)
  Is there an error in this question or solution?
Chapter 9: Differentiation - Miscellaneous Exercise 9 [Page 123]

APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) [English] 11 Standard Maharashtra State Board
Chapter 9 Differentiation
Miscellaneous Exercise 9 | Q I. (5) | Page 123

RELATED QUESTIONS

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


Find the derivative of the following function by the first principle: `x sqrtx`


Differentiate the following function w.r.t.x. : `"e"^x/("e"^x + 1)`


Differentiate the following function w.r.t.x. : `((2"e"^x - 1))/((2"e"^x + 1))`


Differentiate the following function w.r.t.x. : `((x+1)(x-1))/(("e"^x+1))`


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 total cost of producing x units is given by C = 10e2x, find its marginal cost and average cost when x = 2.


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. : `xsqrt x`


Find `dy/dx if y = x^2 + 1/x^2`


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/-.


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 = `sqrt(x) + tan x - x^3`


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 = `x^(7/3) + 5x^(4/5) - 5/(x^(2/5))`


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)` =


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×