y’=sinπ(2x+3)
The given equation is y’ = sin(π(2x+3))
The given equation is y’ = sin(π(2x+3)).
To solve this equation, you need to find the derivative of y with respect to x.
The derivative of sin(π(2x+3)) can be found using the chain rule. According to the chain rule, if you have a composite function f(g(x)), the derivative will be f'(g(x)) * g'(x).
In this case, g(x) = π(2x+3) and f(x) = sin(x).
Taking the derivative of g(x) with respect to x, you get g'(x) = 2π.
Taking the derivative of f(x) with respect to x, you get f'(x) = cos(x).
Now, applying the chain rule, you can find the derivative of y’ with respect to x.
y’ = f'(g(x)) * g'(x)
= cos(π(2x+3)) * 2π
So, the derivative of y with respect to x is y’ = 2πcos(π(2x+3)).
This means that the rate of change of y with respect to x is given by the function 2πcos(π(2x+3)).
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