Math  /  Calculus

Questionsin(x+y)=3x\sin(x+y) = 3x Find dydx\frac{dy}{dx}.

Studdy Solution
Set the derivatives equal to each other:
cos(x+y)(1+dydx)=3 \cos(x+y) \cdot \left(1 + \frac{dy}{dx}\right) = 3
Solve for dydx\frac{dy}{dx}:
cos(x+y)+cos(x+y)dydx=3 \cos(x+y) + \cos(x+y) \cdot \frac{dy}{dx} = 3
Subtract cos(x+y)\cos(x+y) from both sides:
cos(x+y)dydx=3cos(x+y) \cos(x+y) \cdot \frac{dy}{dx} = 3 - \cos(x+y)
Divide both sides by cos(x+y)\cos(x+y) to isolate dydx\frac{dy}{dx}:
dydx=3cos(x+y)cos(x+y) \frac{dy}{dx} = \frac{3 - \cos(x+y)}{\cos(x+y)}
The derivative dydx\frac{dy}{dx} is 3cos(x+y)cos(x+y)\boxed{\frac{3 - \cos(x+y)}{\cos(x+y)}}.

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