Example
Let `f \left( x \right) = 2 x^{4}`.
It is made of a constant `c = 2` and a power function `u \left( x \right) = x^{4}`.
The function `u \left( x \right) = x^{4}` is a power function `x^{n}` with `n=4`. Apply the power rule $$ \begin{align*} u' \left( x \right) &= 4 x ^{4-1} \\ &= 4 x^{3} \end{align*} $$
So the derivative of `f \left( x \right)` is $$ \begin{align*} f' \left( x \right) &= 2 u' \left( x \right) \\ &= 2 \times 4 x ^{3} \\ &= 8 x^{3} \end{align*} $$
Question
What is the derivative of `f \left( x \right) = \frac{ 7 }{ 9 } x^{ 844 }` ?
The function `f \left( x \right) = \frac{ 7 }{ 9 } x^{ 844 }` is made of a constant `c = \frac{ 7 }{ 9 }` and a function `u \left( x \right) = x^{ 844 }`.
The function `u \left( x \right) = x^{ 844 }` looks like `x^{ n }`. Use the power rule with `n = 844` $$ \begin{align*} u' \left( x \right) &= 844 x^{ 844 - 1 } \\ &= 844 x^{ 843 } \end{align*} $$
Therefore, $$ \begin{align*} f' \left( x \right) &= c u' \left( x \right) \\ &= \frac{ 7 }{ 9 } \times 844 x^{ 843 } \\ &= \frac{ 5908 }{ 9 } \times x^{ 843 } \end{align*} $$