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f(x)=x^(2)-8x+16

$f(x)=x^{2}-8 x+16$

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Find derivatives using the chain rule II

Full solution

Q.

f(x)=x^{2}-8 x+16

Identify function: Identify the function to differentiate. $f(x) = x^2 - 8x + 16$
Apply power rule: Apply the power rule to the first term $x^2$ . The power rule states that the derivative of $x^n$ is $n*x^{(n-1)}$ . $\newline$ The derivative of $x^2$ is $2*x^{(2-1)} = 2x$ .
Apply constant multiple rule: Apply the constant multiple rule and power rule to the second term $-8x$ . The constant multiple rule states that the derivative of a constant times a function is the constant times the derivative of the function. The power rule for $x$ is that the derivative of $x$ is $1$ . The derivative of $-8x$ is $-8 \times 1 = -8$ .
Recognize constant term: Recognize that the third term $16$ is a constant, and the derivative of a constant is $0$ . The derivative of $16$ is $0$ .
Combine derivatives: Combine the derivatives of all terms to find the derivative of the entire function. $\newline$ $f'(x) = 2x - 8 + 0$
Simplify derivative: Simplify the derivative expression. $f'(x) = 2x - 8$

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