2 soru [ (a_(n))=(-n^2+2 n+15) ] dizisinin kacines terimi pozitifir

The given equation is:<br /><br />\[ 2 \sin(x) = -x^2 + 2x + 15 \]<br /><br />To find the derivative of this function, we need to differentiate both sides with respect to \( x \).<br /><br />First, let's rewrite the equation in a more standard form:<br /><br />\[ y = 2 \sin(x) \]<br />\[ g(x) = -x^2 + 2x + 15 \]<br /><br />Now, we need to find the derivative of \( y \) and \( g(x) \) with respect to \( x \).<br /><br />1. Differentiate \( y = 2 \sin(x) \):<br /><br />\[ \frac{dy}{dx} = 2 \cos(x) \]<br /><br />2. Differentiate \( g(x) = -x^2 + 2x + 15 \):<br /><br />\[ \frac{d}{dx}(-x^2 + 2x + 15) = -2x + 2 \]<br /><br />So, the derivative of the given function \( 2 \sin(x) = -x^2 + 2x + 15 \) with respect to \( x \) is:<br /><br />\[ \frac{d}{dx}(2 \sin(x)) = -2x + 2 \]<br /><br />Therefore, the derivative of the function is \( -2x + 2 \).