Question

Using chain rule with product or quotient, find the following equation

Answer 1

f'(1) = 7.5

Explanation:

We have the following function:

`f\left(x\right)=3x√(x^3)`

The first thing is to derive the function, just like this:

`\begin{gathered} f^(\prime)(x)=3(d)/(dx)\left(x√(x^3)\right) \\ \\ f^(\prime)(x)=3\left((d)/(dx)\left(x\right)√(x^3)+(d)/(dx)\left(√(x^3)\right)x\right) \\ \\ f^(\prime)(x)=3\left(1\cdot√(x^3)+(3√(x))/(2)\cdot x\right) \\ \\ f^(\prime)(x)=3√(x^3)+(9)/(2)√(x^3) \\ \\ f^(\prime)(x)=(15)/(2)√(x^3) \end{gathered}`

Now, we evaluate when x = 1:

`\begin{gathered} f^(\prime)(x)=(15)/(2)√((1)^3) \\ \\ \begin{equation*} f^(\prime)(x)=(15)/(2) \end{equation*} \end{gathered}`

The result is equal to 15/2 or 7.5