Find the derivative: Write answers without negative or rational exponents.
f (x)= 2
g (x) = 3x(4power)+ 6x(3power)-1
Susie Pre-Calculus
since constants do not change,
f' = 0
Or, if you want to use the power rule,
f = 2 x^0
f' = 0 * x^-1 = 0
g = 3x^4+6x^3-1
g' = 12x^3+18x^2
To find the derivative of a function, you can use the power rule and the constant rule.
For the function f(x) = 2, the derivative is 0 since the derivative of a constant is always 0.
For the function g(x) = 3x^4 + 6x^3 - 1, we can find the derivative term by term using the power rule and the constant rule.
The power rule states that if we have a term of the form x^n, the derivative will be n*x^(n-1).
Applying the power rule, the derivative of 3x^4 is 4*3x^(4-1) = 12x^3.
Similarly, the derivative of 6x^3 is 3*6x^(3-1) = 18x^2.
Since -1 is a constant term, the derivative of -1 is 0.
Therefore, the derivative of g(x) is 12x^3 + 18x^2 + 0, or simply 12x^3 + 18x^2.
Thus, the derivative of f(x) is 0 and the derivative of g(x) is 12x^3 + 18x^2.