Question

Hi, I need help differentiating using the product rule, thanks

Answer 1

Differentiate using the product rule:

g. We take out the constant:

`4(dy)/(dx)\left(x\left(3x-2\right)^5\right)`

So:

`=4\left((d)/(dx)\left(x\right)\left(3x-2\right)^5+(d)/(dx)\left(\left(3x-2\right)^5\right)x\right)`

Now

`\begin{gathered} (d)/(dx)\left(x\right)=1 \\ (d)/(dx)\left(\left(3x-2\right)^5\right)=5(3x-2)^4\cdot(d)/(dx)\left(\left(3x-2\right)^5\right)=5\left(3x-2\right)^4\cdot\:3=15\left(3x-2\right)^4 \end{gathered}`

Substituting the derivatives found:

`=4\left(1\cdot\left(3x-2\right)^5+15\left(3x-2\right)^4x\right)`

Simplify:

`=4\left(\left(3x-2\right)^5+15x\left(3x-2\right)^4\right)`

Answer:

`=4\left(\left(3x-2\right)^5+15x\left(3x-2\right)^4\right)`