(d)/(dx)((1)/(x^(12)))=

Rewrite function: We are asked to find the derivative of the function f(x) = (1)/(x^(12)) with respect to x. To do this, we will use the power rule for differentiation, which states that the derivative of x^n with respect to x is n*x^(n-1). In this case, we can rewrite the function as f(x) = x^(-12) to apply the power rule.Apply power rule: Applying the power rule, we differentiate x^(-12) with respect to x. According to the power rule, the derivative of x^n is n*x^(n-1). Therefore, the derivative of x^(-12) is -12*x^(-12-1) or -12*x^(-13).Rewrite derivative: We can rewrite the derivative in a more conventional form by moving the negative exponent back to the denominator. So, the derivative -12*x^(-13) becomes -12/(x^(13)).Final answer: We have found the derivative of the function (1)/(x^(12)) with respect to x, which is -12/(x^(13)). This is the final answer.

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$\frac{d}{d x}\left(\frac{1}{x^{12}}\right)=$

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Algebra 1

Multiplication with rational exponents

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\frac{d}{d x}\left(\frac{1}{x^{12}}\right)=

Rewrite function: We are asked to find the derivative of the function $f(x) = \frac{1}{x^{12}}$ with respect to $x$ . To do this, we will use the power rule for differentiation, which states that the derivative of $x^n$ with respect to $x$ is $n\cdot x^{(n-1)}$ . In this case, we can rewrite the function as $f(x) = x^{-12}$ to apply the power rule.
Apply power rule: Applying the power rule, we differentiate $x^{-12}$ with respect to $x$ . According to the power rule, the derivative of $x^n$ is $n*x^{n-1}$ . Therefore, the derivative of $x^{-12}$ is $-12*x^{-12-1}$ or $-12*x^{-13}$ .
Rewrite derivative: We can rewrite the derivative in a more conventional form by moving the negative exponent back to the denominator. So, the derivative $-12x^{-13}$ becomes $-\frac{12}{x^{13}}$ .
Final answer: We have found the derivative of the function $(1)/(x^{12})$ with respect to $x$ , which is $-12/(x^{13})$ . This is the final answer.