Question

Differentiate. I have the answer in blue but I don’t know how to take the derivative of the last two term, so please show work.

Answer 1

1) Let's Differentiate the function below applying the Power Rule.

2) Let's rewrite those radicals as powers firstly

`\begin{gathered} f(x)=9x^3-6\sqrt[]{x}+(3)/(x^3)-\frac{5}{\sqrt[4]{x}} \\ f(x)\text{ = }9x^3-6x^{(1)/(2)}+3x^{-3\text{ }}-5x^{(-1)/(4)} \end{gathered}`

3) Let's apply the Power Rule now, subtracting one unit from the exponent and multiplying the base by the original exponent

`f^(\prime)(x)=27x^2-3x^{-\frac{1}{2\text{ }}}-9x^(-4)+(5)/(4)x^{-(5)/(4)}`