Find dydxdydx, if : x = sinθ, y = tanθ - Mathematics and Statistics

Question

Find `"dy"/"dx"`, if : x = sinθ, y = tanθ

Sum

Solution

x = sinθ, y = tanθ
Differentiating x and y w.r.t. x, we get
`"dx"/"dθ" = "d"/"dθ"(sinθ)` = cosθ
and
`"dy"/"dθ" = "d"/"dθ"(tanθ)` = sec²θ

`"dy"/"dx" = (("dy"/"dθ"))/(("dx"/"dθ")`

= `sec^2θ/cosθ`
= sec³θ.

shaalaa.com

Derivatives of Implicit Functions

Is there an error in this question or solution?

Q 1.4 Q 1.3 Q 1.5

Chapter 1: Differentiation - Exercise 1.4 [Page 48]

APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) [English] 12 Standard HSC Maharashtra State Board

Chapter 1 Differentiation
Exercise 1.4 | Q 1.4 | Page 48

Video TutorialsVIEW ALL [3]

view
Video Tutorials For All Subjects
Derivatives of Implicit Functions

video tutorial00:07:07
Derivatives of Implicit Functions

video tutorial00:32:28
Derivatives of Implicit Functions

video tutorial00:25:40

RELATED QUESTIONS

Find `dy/dx` in the following:

2x + 3y = sin x

Find `dx/dy` in the following.

x² + xy + y² = 100

Find `dy/dx` in the following:

sin² y + cos xy = k

if `(x^2 + y^2)^2 = xy` find `(dy)/(dx)`

Show that the derivative of the function f given by

\[f\left( x \right) = 2 x^3 - 9 x^2 + 12x + 9\], at x = 1 and x = 2 are equal.

If for the function

\[\Phi \left( x \right) = \lambda x^2 + 7x - 4, \Phi'\left( 5 \right) = 97, \text { find } \lambda .\]

If \[f\left( x \right) = x^3 + 7 x^2 + 8x - 9\]

, find f'(4).

Find the derivative of the function f defined by f (x) = mx + c at x = 0.

If f (x) = |x − 2| write whether f' (2) exists or not.

Write the derivative of f (x) = |x|³ at x = 0.

Write the value of the derivative of f (x) = |x − 1| + |x − 3| at x = 2.

If x = tan^-1t and y = t³ , find `(dy)/(dx)`.

Discuss extreme values of the function f(x) = x.logx

If `sin^-1((x^5 - y^5)/(x^5 + y^5)) = pi/(6), "show that" "dy"/"dx" = x^4/(3y^4)`

Find `"dy"/"dx"` if x = at², y = 2at.

Find `"dy"/"dx"` if x = a cot θ, y = b cosec θ

Find `"dy"/"dx"`, if : x = `sqrt(a^2 + m^2), y = log(a^2 + m^2)`

Find `"dy"/"dx"`, if : x = a(1 – cosθ), y = b(θ – sinθ)

Find `"dy"/"dx"`, if : x = `(t + 1/t)^a, y = a^(t+1/t)`, where a > 0, a ≠ 1, t ≠ 0.

Find `"dy"/"dx"`, if : `x = cos^-1((2t)/(1 + t^2)), y = sec^-1(sqrt(1 + t^2))`

Find `"dy"/"dx"`, if : `x = cos^-1(4t^3 - 3t), y = tan^-1(sqrt(1 - t^2)/t)`.

Find `dy/dx` if : x = 2 cos t + cos 2t, y = 2 sin t – sin 2t at t = `pi/(4)`

Find `"dy"/"dx"` if : x = t + 2sin (πt), y = 3t – cos (πt) at t = `(1)/(2)`

DIfferentiate x sin x w.r.t. tan x.

Differentiate `sin^-1((2x)/(1 + x^2))w.r.t. cos^-1((1 - x^2)/(1 + x^2))`

Differentiate x^x w.r.t. x^six.

Differentiate `tan^-1((sqrt(1 + x^2) - 1)/(x)) w.r.t tan^-1((2xsqrt(1 - x^2))/(1 - 2x^2))`.

If x = at² and y = 2at, then show that `xy(d^2y)/(dx^2) + a` = 0.

If x² + 6xy + y² = 10, show that `(d^2y)/(dx^2) = (80)/(3x + y)^3`.

If x = a sin t – b cos t, y = a cos t + b sin t, show that `(d^2y)/(dx^2) = -(x^2 + y^2)/(y^3)`.

Find the n^th derivative of the following : (ax + b)^m

Find the n^th derivative of the following:

`(1)/x`

Find the nth derivative of the following : a^px+q

Find the n^th derivative of the following : sin (ax + b)

Find the n^th derivative of the following:

y = e^8x . cos (6x + 7)