Using the product rule, differentiate y=(2x)(e^3x)

The product rule states that if y=uv, where u and v are both functions of x, then dy/dx = u(dv/dx) + v(du/dx)Therefore, the differential of 2xe3x can be found by letting 2x=u and e3x =v.u=2x,du/dx = 2
v=e3xdv/dx = 3e3x
dy/dx = u(dv/dx) + v(du/dx)dy/dx = 2x(3e3x) + e3x(2)dy/dx = 6xe3x + 2e3xdy/dx = 2e3x(3x+1)

CO
Answered by Christy O. Maths tutor

5846 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Consider the curve y=x/(x+4)^0.5. (i) Show that the derivative of the curve is given by dy/dx= (x+8)/2(x+4)^3/2 and (ii) hence find the coordinates of the intersection between the left vertical asymptote and the line tangent to the curve at the origin.


Find the range of a degree-2 polynomial function such as 2x^2 +1, or x^2 + 2x - 3.


What are the solutions of (x^3)+6 = 2(x^2)+5x given x = 3 is a solution?


Express: (x^2 + 5x - 14) / (2x^2 - 4x) as a fraction in it's simplest form.


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