हिंदी

Differentiate the following w.r.t.x : y = x43+ex-sinx

Advertisements
Advertisements

प्रश्न

Differentiate the following w.r.t.x :

y = `x^(4/3) + "e"^x - sinx`

योग
Advertisements

उत्तर

y = `x^(4/3) + "e"^x - sinx`

Differentiating w.r.t. x, we get

`("d"y)/("d"x) = "d"/("d"x)(x^(4/3) + "e"^x - sinx)`

∴ `("d"y)/("d"x) = "d"/("d"x) (x^(4/3)) + "d"/("d"x)("e"^x) - "d"/("d"x)(sinx)`

= `4/3x^(4/3 - 1) + "e"^x - cos x`

= `4/3 x^(1/3) + "e"^x - cos x`

shaalaa.com
Rules of Differentiation (Without Proof)
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 9: Differentiation - Exercise 9.2 [पृष्ठ १९२]

APPEARS IN

बालभारती Mathematics and Statistics (Arts and Science) Part 2 [English] Standard 11 Maharashtra State Board
अध्याय 9 Differentiation
Exercise 9.2 | Q I. (1) | पृष्ठ १९२

संबंधित प्रश्न

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. : `x/(x + 1)`


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. : `"e"^x/("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))`


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.


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 supply S for a commodity at price P is given by S = P2 + 9P − 2. Find the marginal supply when price is 7/-.


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


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


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


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 = "e"^x/logx`


The relation between price (P) and demand (D) of a cup of Tea is given by D = `12/"P"`. Find the rate at which the demand changes when the price is Rs. 2/-. Interpret the result.


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 = `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))`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×