Find the derivative of f(x)=x^2*e^x+x

You can split the derivative into 2 parts: dx/dy (x^2*e^x) + dx/dy (x)

For the first part you have to use the product rule, so let U=x^2 V=e^x U'=2x V'=Chain rule

V'=dx/dy(e^x)dx/dy(x)=e^x1=e^x

Returning to the product rule, f'(x)=U'V+UV' So, (2xe^x)+(x^2e^x) =x(x+2)e^x

Second part is dx/dy(x)=1

Final answer =x(x+2)e^x+1

Answered by Benedict R. Maths tutor

3318 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

What is greater e^pi or pi^e?


Given that y = 4x^3 -1 + 2x^1/2 (where x>0) find dy/dx.


d/dx[sin(x) + cos(x)]


Define the derivative of a function f(x) and use this to calculate the derivative of f(x)=x^n for positive integer n.


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences