हिंदी
तमिलनाडु बोर्ड ऑफ सेकेंडरी एज्युकेशनएचएससी विज्ञान कक्षा ११

Find the derivatives of the following: abx2a2+y2b2 = 1

Advertisements
Advertisements

प्रश्न

Find the derivatives of the following:

`x^2/"a"^2 + y^2/"b"^2` = 1

योग
Advertisements

उत्तर

`x^2/"a"^2 + y^2/"b"^2` = 1

`(2x)/"a"^2 + (2y)/"b"^2 ("d"y)/("d"x)` = 0

`(2y)/"b"^2 ("d"y)/("d"x) = - (2x)/"a"^2`

`("d"y)/("d"x) = - (2x)/"a"^2 xx "b"^2/(2y)`

`("d"y)/("d"x) = - "b"^2/"a"^2 x/y`

shaalaa.com
Differentiation Rules
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 10: Differential Calculus - Differentiability and Methods of Differentiation - Exercise 10.4 [पृष्ठ १७६]

APPEARS IN

सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 11 TN Board
अध्याय 10 Differential Calculus - Differentiability and Methods of Differentiation
Exercise 10.4 | Q 6 | पृष्ठ १७६

संबंधित प्रश्न

Find the derivatives of the following functions with respect to corresponding independent variables:

f(x) = x – 3 sin x


Find the derivatives of the following functions with respect to corresponding independent variables:

y = sin x + cos x


Find the derivatives of the following functions with respect to corresponding independent variables:

y = x sin x cos x


Find the derivatives of the following functions with respect to corresponding independent variables:

y = e-x . log x


Differentiate the following:

h(t) = `("t" - 1/"t")^(3/2)`


Differentiate the following:
y = cos (a3 + x3)


Differentiate the following:
y = e–mx 


Differentiate the following:

y = `(x^2 + 1) root(3)(x^2 + 2)`


Differentiate the following:
y = sin3x + cos3x


Find the derivatives of the following:
y = `x^(logx) + (logx)^x`


Find the derivatives of the following:
`sqrt(x) = "e"^((x - y))`


Find the derivatives of the following:

(cos x)log x


Find the derivatives of the following:

`tan^-1 = ((6x)/(1 - 9x^2))`


Find the derivatives of the following:

x = `(1 - "t"^2)/(1 + "t"^2)`, y = `(2"t")/(1 + "t"^2)`


Find the derivatives of the following:

Find the derivative of sin x2 with respect to x2 


Find the derivatives of the following:

If u = `tan^-1  (sqrt(1 + x^2) - 1)/x` and v = `tan^-1 x`, find `("d"u)/("d"v)`


Find the derivatives of the following:

If x = a(θ + sin θ), y = a(1 – cos θ) then prove that at θ = `pi/2`, yn = `1/"a"`


Choose the correct alternative:

If y = `1/4 u^4`, u = `2/3 x^3 + 5`, then `("d"y)/("d"x)` is 


Choose the correct alternative:

If y = `1/("a" - z)`, then `("d"z)/("d"y)` is


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×