Identify function: Identify the function to differentiate. The function is y=(-x^(2)-16x)-30.Rewrite function: Rewrite the function for clarity. The function can be written as y = -x^2 - 16x - 30.Differentiate -x^2: Differentiate the first term, -x^2, with respect to x. The derivative of -x^2 with respect to x is -2x.Differentiate -16x: Differentiate the second term, -16x, with respect to x. The derivative of -16x with respect to x is -16.Differentiate constant: Differentiate the constant term, -30, with respect to x. The derivative of a constant is 0.Combine derivatives: Combine the derivatives of the terms to get the derivative of the entire function. The derivative of y = -x^2 - 16x - 30 is dy/dx = -2x - 16.

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$y=\left(-x^{2}-16 x\right)-30$

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Calculus

Find derivatives using the chain rule I

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y=\left(-x^{2}-16 x\right)-30

Identify function: Identify the function to differentiate. The function is $y=(-x^{2}-16x)-30$ .
Rewrite function: Rewrite the function for clarity. The function can be written as $y = -x^2 - 16x - 30$ .
Differentiate $-x^2$ : Differentiate the first term, $-x^2$ , with respect to $x$ . The derivative of $-x^2$ with respect to $x$ is $-2x$ .
Differentiate $-16x$ : Differentiate the second term, $-16x$ , with respect to $x$ . The derivative of $-16x$ with respect to $x$ is $-16$ .
Differentiate constant: Differentiate the constant term, $-30$ , with respect to $x$ . The derivative of a constant is $0$ .
Combine derivatives: Combine the derivatives of the terms to get the derivative of the entire function. The derivative of $y = -x^2 - 16x - 30$ is $\frac{dy}{dx} = -2x - 16$ .