हिंदी
तमिलनाडु बोर्ड ऑफ सेकेंडरी एज्युकेशनएचएससी विज्ञान कक्षा ११

Differentiate the following:y = sin(tan(sinx))

Advertisements
Advertisements

प्रश्न

Differentiate the following:
y = `sin(tan(sqrt(sinx)))`

योग
Advertisements

उत्तर

y = `sin(tan(sqrt(sinx)))`

y = f(g(x))

`("d"y)/("d"x)` = f'(g(x)) . g'(x)

`("d"y)/("d"x) = cos(tan(sqrt(sinx))) sec^2(sqrt(sinx)) xx 1/2(sinx)^(1/2 - 1) cos x`

`("d"y)/("d"x) = 1/2 cos (tan(sqrt(sinx))) sec^2 (sqrt(sinx)) (sinx)^(- 1/2) cosx`

`("d"y)/("d"x) = (cos(tan(sqrt(sinx))) sec^2(sqrt(sinx)) cosx)/(2(sinx)^(1/2)`

shaalaa.com
Differentiation Rules
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 10: Differential Calculus - Differentiability and Methods of Differentiation - Exercise 10.3 [पृष्ठ १६४]

APPEARS IN

सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 11 TN Board
अध्याय 10 Differential Calculus - Differentiability and Methods of Differentiation
Exercise 10.3 | Q 29 | पृष्ठ १६४

संबंधित प्रश्न

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

g(t) = 4 sec t + tan t


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

y = `tan x/x`


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

y = `(tanx - 1)/secx`


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

y = x sin x cos x


Differentiate the following:
y = sin (ex)


Differentiate the following:
y = e–mx 


Differentiate the following:
y = 4 sec 5x


Differentiate the following:
y = (2x – 5)4 (8x2 – 5)–3 


Differentiate the following:

y = `x"e"^(-x^2)`


Differentiate the following:

f(x) = `x/sqrt(7 - 3x)`


Differentiate the following:
y = (1 + cos2)6


Find the derivatives of the following:

(cos x)log x


Find the derivatives of the following:

x = `"a" cos^3"t"` ; y = `"a" sin^3"t"`


Find the derivatives of the following:

x = a (cos t + t sin t); y = a (sin t – t cos t)


Find the derivatives of the following:

If y = sin–1x then find y”


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


Choose the correct alternative:

If y = `(1 - x)^2/x^2`, then `("d"y)/("d"x)` is


Choose the correct alternative:

If f(x) = `{{:(x - 5,  "if"  x ≤ 1),(4x^2 - 9,  "if"  1 < x < 2),(3x + 4,  "if"  x ≥ 2):}` , then the right hand derivative of f(x) at x = 2 is


Choose the correct alternative:

If f(x) = `{{:(2"a" - x,  "for"  - "a" < x < "a"),(3x - 2"a", "for"  x ≥ "a"):}` , then which one of the following is true?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×