Find {eq}f'(x) {/eq}, when {eq}\displaystyle f(x) = \frac{1}{3} x^6 - 6x^4 + 8x {/eq}.

Question:

Differentiation of f(x):

Consider the function {eq}\displaystyle u = f(t), {/eq} where {eq}\displaystyle u {/eq} is dependent variable and {eq}\displaystyle t {/eq} is independent variable. Then derivative of {eq}\displaystyle u {/eq} with respect to {eq}\displaystyle t {/eq} is defined by

{eq}\displaystyle \frac{du}{dt} = \frac{d}{dt} (f(t)) = f'(t). {/eq}

We recall the following formula in the given problem:

{eq}\displaystyle \frac{d}{{dx}}\left( {{x^n}} \right) = n{x^{n - 1}}. {/eq}

Answer and Explanation: 1