हिंदी

Find dydxif y = x log x (x2 + 1) - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Find `dy/dx`if y = x log x (x2 + 1)

योग
Advertisements

उत्तर

y = x log x (x2 + 1)
Differentiating w.r.t. x, we get

`dy/dx = d/dx(x)(logx)(x^2 + 1)`

= `(x)(logx)d/dx(x^2 + 1) - (x^2 + 1)d/dx((x)(logx))`

= `(xlogx)(2x + 0) + (x^2 + 1)[xd/dx(logx) + (logx)d/dx(x)]`

=`2x^2logx + (x^2 + 1)[x xx 1/x + (logx)(1)]`

= 2x2 log x + (x2 + 1) (1 + log x)
= 2x2 log x + (x2 + 1) + (x2 + 1) log x

shaalaa.com
Rules of Differentiation (Without Proof)
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 9: Differentiation - Miscellaneous Exercise 9 [पृष्ठ १२३]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Commerce) [English] Standard 11 Maharashtra State Board
अध्याय 9 Differentiation
Miscellaneous Exercise 9 | Q II. (10) | पृष्ठ १२३

संबंधित प्रश्न

Find the derivative of the following w. r. t. x. : `(xe^x)/(x+e^x)`


Find the derivative of the following function by the first principle: 3x2 + 4


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


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


Differentiate the following function w.r.t.x. : `2^x/logx`


Differentiate the following function w.r.t.x. : `((x+1)(x-1))/(("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: 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: 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. : x5


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


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 = `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)` =


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×