मराठी
तामिळनाडू बोर्ड ऑफ सेकेंडरी एज्युकेशनएचएससी विज्ञान इयत्ता ११

Find the derivatives of the following functions with respect to corresponding independent variables: y = tan θ (sin θ + cos θ) - Mathematics

Advertisements
Advertisements

प्रश्न

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

y = tan θ (sin θ + cos θ)

बेरीज
Advertisements

उत्तर

y = tan θ (sin θ + cos θ)

`("d"y)/("d"x)` = tan θ (cos θ – sin θ) + (sin θ + cos 0) sec2 θ

= tan θ cos θ – tan θ sin θ + sin θ sec2θ + cos θ sec2θ

= `tan theta cos theta - tan theta sin theta + sintheta/(cos^2theta) + costheta/(cos^2theta)`

= `sin theta/cos theta cos theta - sin theta/cos theta sin theta + sin theta/cos theta * 1/cos theta + 1/costheta`

= sin θ – sin2θ sec θ + tan θ sec θ + sec θ

= sin θ + (1 – sin2θ) sec θ + sec θ tan θ

= `sin theta + cos^2theta xx 1/cos theta + sectheta tan theta`

= sin θ + cos θ + sec θ tan θ

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 13 | पृष्ठ १६०

संबंधित प्रश्‍न

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

y = `sinx/x^2`


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

y = (x2 + 5) log(1 + x) e–3x 


Differentiate the following:
y = tan 3x


Differentiate the following:

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


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


Differentiate the following:
y = tan (cos x)


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


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


Find the derivatives of the following:

(cos x)log x


Find the derivatives of the following:

`cos[2tan^-1 sqrt((1 - x)/(1 + x))]`


Find the derivatives of the following:

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


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:

sin-1 (3x – 4x3)


Find the derivatives of the following:

Find the derivative with `tan^-1 ((sinx)/(1 + cos x))` with respect to `tan^-1 ((cosx)/(1 + sinx))`


Find the derivatives of the following:

If y = `(sin^-1 x)/sqrt(1 - x^2)`, show that (1 – x2)y2 – 3xy1 – y = 0


Find the derivatives of the following:

If y = `(cos^-1 x)^2`, prove that `(1 - x^2) ("d"^2y)/("d"x)^2 - x ("d"y)/("d"x) - 2` = 0. Hence find y2 when x = 0


Choose the correct alternative:

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


Choose the correct alternative:

The number of points in R in which the function f(x) = |x – 1| + |x – 3| + sin x is not differentiable, is


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×