flatantsmu

2022-10-08

How do you differentiate $y\mathrm{sin}x=y$

trutdelamodej0

Beginner2022-10-09Added 11 answers

You can use the product rule, like the usual. Just remember that the derivative of y with respect to x in $\frac{df}{dx}$ is $\frac{dy}{dx}$

With $f\left(x\right):y\mathrm{sin}x=y$

$\frac{df}{dx}[y\mathrm{sin}x=y]=y\mathrm{cos}x+\mathrm{sin}x\left(\frac{dy}{dx}\right)=\frac{dy}{dx}$

$\frac{dy}{dx}[1-\mathrm{sin}x]=y\mathrm{cos}x$

$\frac{dy}{dx}=\frac{y\mathrm{cos}x}{1-\mathrm{sin}x}$

If you check Wolfram Alpha, you'll see this, just multiplied by −1.

With $f\left(x\right):y\mathrm{sin}x=y$

$\frac{df}{dx}[y\mathrm{sin}x=y]=y\mathrm{cos}x+\mathrm{sin}x\left(\frac{dy}{dx}\right)=\frac{dy}{dx}$

$\frac{dy}{dx}[1-\mathrm{sin}x]=y\mathrm{cos}x$

$\frac{dy}{dx}=\frac{y\mathrm{cos}x}{1-\mathrm{sin}x}$

If you check Wolfram Alpha, you'll see this, just multiplied by −1.

What is the derivative of the work function?

How to use implicit differentiation to find $\frac{dy}{dx}$ given $3{x}^{2}+3{y}^{2}=2$?

How to differentiate $y=\mathrm{log}{x}^{2}$?

The solution of a differential equation y′′+3y′+2y=0 is of the form

A) ${c}_{1}{e}^{x}+{c}_{2}{e}^{2x}$

B) ${c}_{1}{e}^{-x}+{c}_{2}{e}^{3x}$

C) ${c}_{1}{e}^{-x}+{c}_{2}{e}^{-2x}$

D) ${c}_{1}{e}^{-2x}+{c}_{2}{2}^{-x}$How to find instantaneous velocity from a position vs. time graph?

How to implicitly differentiate $\sqrt{xy}=x-2y$?

What is 2xy differentiated implicitly?

How to find the sum of the infinite geometric series given $1+\frac{2}{3}+\frac{4}{9}+...$?

Look at this series: 1.5, 2.3, 3.1, 3.9, ... What number should come next?

A. 4.2

B. 4.4

C. 4.7

D. 5.1What is the derivative of $\frac{x+1}{y}$?

How to find the sum of the infinite geometric series 0.9 + 0.09 + 0.009 +…?

How to find the volume of a cone using an integral?

What is the surface area of the solid created by revolving $f\left(x\right)={e}^{2-x},x\in [1,2]$ around the x axis?

How to differentiate ${x}^{\frac{2}{3}}+{y}^{\frac{2}{3}}=4$?

The differential coefficient of $\mathrm{sec}\left({\mathrm{tan}}^{-1}\left(x\right)\right)$.