Question

(2) Use the correct formula above to find the derivative of the function

Answer 1

Using Product rule

Given

`f(x)=(x^6+14)\sqrt[]{x}`

Solution

Applying Product Rule

`\begin{gathered} =(d)/(dx)\mleft(x^6+14\mright)√(x)+(d)/(dx)\mleft(√(x)\mright)\mleft(x^6+14\mright) \\ \\ \\ (d)/(dx)(x^6+14)=6x^5 \\ \\ (d)/(dx)(\sqrt[]{x})=(1)/(2√(x)) \end{gathered}`
`(d)/(dx)(x^6+14)\sqrt[]{x}+(d)/(dx)(\sqrt[]{x})(x^6+14)=6x^5√(x)+(1)/(2√(x))\mleft(x^6+14\mright)`

Simplify

`=(13x^6+14)/(2√(x))`

The final answer

`=(13x^6+14)/(2√(x))`