If y = cos(x^{circ}) and z = cos x,then frac{ | vedclass

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

Question

(C) Given $y = \cos(x^{\circ})$ and $z = \cos x$. Since $x^{\circ} = \frac{\pi x}{180}$ radians,we have $y = \cos\left(\frac{\pi x}{180}\right)$. Diff

Vedclass · Accepted Answer

$\frac{\pi}{180} \sin(x^{\circ}) \operatorname{cosec} x$

Vedclass · Answer

(C) Given $y = \cos(x^{\circ})$ and $z = \cos x$. Since $x^{\circ} = \frac{\pi x}{180}$ radians,we have $y = \cos\left(\frac{\pi x}{180}\right)$. Differentiating $y$ with respect to $x$: $\frac{dy}{dx} = -\sin\left(\frac{\pi x}{180}\right) \cdot \frac{\pi}{180} = -\frac{\pi}{180} \sin(x^{\circ})$. Differentiating $z$ with respect to $x$: $\frac{dz}{dx} = -\sin x$. Now,using the chain rule: $\frac{dy}{dz} = \frac{dy/dx}{dz/dx} = \frac{-\frac{\pi}{180} \sin(x^{\circ})}{-\sin x} = \frac{\pi}{180} \sin(x^{\circ}) \operatorname{cosec} x$.

If $y = \cos(x^{\circ})$ and $z = \cos x$,then $\frac{dy}{dz}$ is equal to

Similar Questions

If $f(x) = \frac{x}{1+|x|}$,for $x \in \mathbb{R}$,then $f^{\prime}(0)$ is equal to :

Let $f(x + y) = f(x) + f(y)$ and $f(x) = x^2 g(x)$ for all $x, y \in R$,where $g(x)$ is a continuous function. Then $f'(x)$ is equal to

If $y = f \left( \frac{3x + 4}{5x + 6} \right)$ and $f'(x) = \tan(x^2)$,then $\frac{dy}{dx} = $

Let $f : R \rightarrow R$ be defined as $f(x) = x^{3} + x - 5$. If $g(x)$ is a function such that $f(g(x)) = x, \forall x \in R$,then $g^{\prime}(63)$ is equal to

If $y = \frac{1}{a - z}$,then $\frac{dz}{dy} = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module