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y=(-x^(2)-16 x)-30

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

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Find derivatives using the chain rule I

Full solution

Q.

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 $\frac{dy}{dx} = -2x - 16$ .

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