Question

Use the product rule to differentiate = y=e^2x(x^4-1)

Answer 1

Given expression

`y=e^(2x)(x^4-1)`

To solve it with product rule. First we will get familiar with product rule. That is

`(d(uv))/(dx)=u(du)/(dv)+v(du)/(dx)`

Now, we will solve given as:

`\begin{gathered} (d(e^(2x)(x^4-1)))/(dx)=e^(2x)(d(x^4-1))/(dx)+(x^4-1)(d(e^(2x)))/(dx) \\ =e^(2x)(4x^3)+(x^4-1)2e^(2x)^{} \\ =4e^(2x)x^3+2e^(2x)x^4-2e^(2x) \end{gathered}`

Hence, we got solution after applying product rule.