मराठी
तामिळनाडू बोर्ड ऑफ सेकेंडरी एज्युकेशनएचएससी विज्ञान इयत्ता ११

Find the derivatives of the following functions with respect to corresponding independent variables: y = sinxx2

Advertisements
Advertisements

प्रश्न

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

y = `sinx/x^2`

बेरीज
Advertisements

उत्तर

y = `sinx/x^2`

`("d"y)/("d"x) = (x^2(cos x) - sin x(2x))/((x^2))`

= `(x^2 cos x - 2x sin x)/x^4`

= `(x[x cos x - 2 sin x])/x^4`

`("d"y)/("d"x) = (x cos x - 2 sin x)/x^3`

shaalaa.com
Differentiation Rules
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 10: Differential Calculus - Differentiability and Methods of Differentiation - Exercise 10.2 [पृष्ठ १६०]

APPEARS IN

सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 11 TN Board
पाठ 10 Differential Calculus - Differentiability and Methods of Differentiation
Exercise 10.2 | Q 12 | पृष्ठ १६०

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:

f(x) = x sin x


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

y = cos x – 2 tan x


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

g(t) = t3 cos t


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

y = `x/(sin x + cosx)`


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

y = tan θ (sin θ + cos θ)


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

Draw the function f'(x) if f(x) = 2x2 – 5x + 3


Differentiate the following:
y = cos (tan x)


Differentiate the following:
y = `"e"^sqrt(x)`


Differentiate the following:
y = e–mx 


Differentiate the following:
y = `sqrt(x +sqrt(x)`


Differentiate the following:
y = `sqrt(x + sqrt(x + sqrt(x)`


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


Differentiate the following:

y = `sin^-1 ((1 - x^2)/(1 + x^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 sin y = x sin(a + y), the prove that `("d"y)/("d"x) = (sin^2("a" + y))/sin"a"`, a ≠ nπ


Choose the correct alternative:

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


Choose the correct alternative:

If y = cos (sin x2), then `("d"y)/("d"x)` at x = `sqrt(pi/2)` is


Choose the correct alternative:

If f(x) = `{{:("a"x^2 - "b"",", - 1 < x < 1),(1/|x|",",  "elsewhere"):}` is differentiable at x = 1, then


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×