48.1k views
0 votes
Can you answer this question.Find the derivative of the given function

Can you answer this question.Find the derivative of the given function-example-1

1 Answer

3 votes

Answer:


(dy)/(dx)\text{ = }3x^2\cdot e^(-x^3)(1-x^3)\text{ }

Step-by-step explanation:

Here, we want to find the derivative of the given function

To do this, we are going to use the product rule

Mathematically, we have the product rule as follows:


(dy)/(dx)\text{ = u}(dv)/(dx)\text{ + v}(du)/(dx)

where:


\begin{gathered} u=x^3 \\ v=e^(-x^3) \end{gathered}

We proceed as follows to find the unit derivatives:


\begin{gathered} (du)/(dx)=3x^2 \\ \\ \text{for }(dv)/(dx) \\ \\ \text{let w = -x}^3 \\ v=e^w \\ (dw)/(dx)=-3x^2 \\ (dv)/(dw)=e^w \\ \\ (dv)/(dx)\text{ = }(dw)/(dx)*(dv)/(dw) \\ \\ =-3x^2* e^w \\ =-3x^2\text{ }* e^(-x^3) \end{gathered}

We put together the final answer as follows:


\begin{gathered} (dy)/(dx)=x^3*(-3x^2* e^(-x^3))+e^(-x^3)(3x^2) \\ \\ \\ (dy)/(dx)=3x^2\cdot e^(-x^3)(-x^3+1) \\ (dy)/(dx)\text{ = }3x^2\cdot e^(-x^3)(1-x^3)\text{ } \end{gathered}

User Keithgaputis
by
8.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories