If x = sin 2theta cos 3theta and y = sin 3the | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given $x = \sin 2	heta \cos 3	heta$ and $y = \sin 3	heta \cos 2	heta$. Differentiating $x$ with respect to $	heta$: $\frac{dx}{d	heta} = \fr

Vedclass · Accepted Answer

$\frac{3\cos 3	heta \cos 2	heta - 2\sin 3	heta \sin 2	heta}{2\cos 2	heta \cos 3	heta - 3\sin 2	heta \sin 3	heta}$

Vedclass · Answer

(B) Given $x = \sin 2	heta \cos 3	heta$ and $y = \sin 3	heta \cos 2	heta$. Differentiating $x$ with respect to $	heta$: $\frac{dx}{d	heta} = \frac{d}{d	heta}(\sin 2	heta \cos 3	heta) = \cos 2	heta(2) \cos 3	heta + \sin 2	heta(-\sin 3	heta)(3) = 2\cos 2	heta \cos 3	heta - 3\sin 2	heta \sin 3	heta$. Differentiating $y$ with respect to $	heta$: $\frac{dy}{d	heta} = \frac{d}{d	heta}(\sin 3	heta \cos 2	heta) = \cos 3	heta(3) \cos 2	heta + \sin 3	heta(-\sin 2	heta)(2) = 3\cos 3	heta \cos 2	heta - 2\sin 3	heta \sin 2	heta$. Using the chain rule, $\frac{dy}{dx} = \frac{dy/d	heta}{dx/d	heta} = \frac{3\cos 3	heta \cos 2	heta - 2\sin 3	heta \sin 2	heta}{2\cos 2	heta \cos 3	heta - 3\sin 2	heta \sin 3	heta}$. Thus, the correct option is $B$.

If $x = \sin 2\theta \cos 3\theta$ and $y = \sin 3\theta \cos 2\theta$, then find $\frac{dy}{dx}$.

Similar Questions

Derivative of $\sin ^2 x$ with respect to $e^{\cos x}$ is

The derivative of $\sec ^{-1}\left(\frac{1}{2 x^2-1}\right)$ with respect to $\sqrt{1-x^2}$ at $x=\frac{1}{2}$ equals

If $x=a t^2$ and $y=2 a t$,then $\frac{d^2 y}{d x^2}$ at $t=\frac{1}{2}$ is

If $x=\sec \theta-\cos \theta$,$y=\sec ^{10} \theta-\cos ^{10} \theta$ and $(x^2+4)(\frac{dy}{dx})^2=k(y^2+4)$,then the value of $k$ is

If $x = \sin t$ and $y = \sin pt$,then the value of $(1 - x^2) \frac{d^2 y}{d x^2} - x \frac{d y}{d x} + p^2 y =$

Vedclass Test Series

Exam Paper Generator

Online Exam Module