Find the derivative of the function f by using the rules of differentiation.
f(x) = x^4 - 4x^2 + 3
f '(x) =??
4x^3 - 8x
To find the derivative of the function f(x) = x^4 - 4x^2 + 3, you can apply the power rule for differentiation. The power rule states that for a function of the form f(x) = x^n, the derivative is given by f'(x) = nx^(n-1).
So, let's apply the power rule to each term of the function f(x):
First term: x^4
The power rule gives us: (4)(x^(4-1)) = 4x^3
Second term: -4x^2
The power rule gives us: (-4)(2)(x^(2-1)) = -8x^1 = -8x
Third term: 3
The derivative of a constant is always zero, so the derivative is simply 0.
Now, sum up the derivatives of the individual terms:
f '(x) = 4x^3 - 8x + 0
Therefore, the derivative of f(x) = x^4 - 4x^2 + 3 is f '(x) = 4x^3 - 8x.