consider the following function.\n\n$f(x)=x^{3}-6x^{2}+12x$\n\nfind the derivative of the function.\n\n$f(x)=…

consider the following function.\n\n$f(x)=x^{3}-6x^{2}+12x$\n\nfind the derivative of the function.\n\n$f(x)=square$

consider the following function.\n\n$f(x)=x^{3}-6x^{2}+12x$\n\nfind the derivative of the function.\n\n$f(x)=square$

Answer

Explanation:

Step1: Apply power - rule to each term

The power - rule states that if $y = ax^n$, then $y^\prime=anx^{n - 1}$. For the term $x^3$, its derivative is $3x^{3-1}=3x^2$. For the term $-6x^2$, its derivative is $-6\times2x^{2 - 1}=-12x$. For the term $12x$, its derivative is $12\times1x^{1 - 1}=12$.

Step2: Combine the derivatives of each term

$f^\prime(x)=3x^2-12x + 12$

Answer:

$3x^2-12x + 12$