Question

find dy/dx when sin(x+y)=2/3​

Answer 1

Step-by-step explanation:

I hope it would help you

Answer 2

Answer:

The value of $\frac{dy}{dx}$ is $-1$ when $sin(x+y)=\frac{2}{3}$.

Step-by-step explanation:

Chain rule for derivative: The chain rule states that the derivative of $f(g(x))$ is $f'(g(x))\cdot g'(x)$.

Generally it helps us to differentiate the composite functions.

Step 1 of 2

Consider the given function ad follows:

$sin(x+y)=\frac{2}{3}$

Differentiate both the sides with respect to $x$ as follows:

$\frac{d}{dx}(sin(x+y))=\frac{d}{dx}(\frac{2}{3} )$

Further, simplify the derivative using chain rule on left-hand side as follows:

$\frac{d}{dx}(sin(x+y))\cdot \frac{d}{dx}(x+y) =0$ (Since derivative of constant is zero)

        $cos(x+y)\cdot (1+\frac{dy}{dx} )=0$

$cos(x+y)+cos(x+y)\frac{dy}{dx}=0$ . . . . . (1)

Step 2 of 2

To find: The value of $dy/dx$.

Rewrite the equation (1) as follows:

⇒ $cos(x+y)\frac{dy}{dx}=-cos(x+y)$

Cancellation of cosine function is possible only when the the value of $cos(x+y)$ is finite.

⇒ $\frac{dy}{dx}=-1$

Therefore, the derivative of the function $sin(x+y)=2/3$ is $-1$.

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