Find the derivative of the function y=3x^2e^(2x)sin(x).

y is the product of three different function, so we would use the product rule in order to calculate the derivative of the curve. In order to apply the product rule we need to find the derivatives of each of the three functions separately. y1=3x2         -->      dy1/dx = 6x [by simply using the chain rule of differentiation] y2=e2x         -->      dy2/dy = 2e2x y3=sin(x)     -->      dy3/dx = cos(x) According to the product rule each function is to be differentiated one at a time and the other functions remain unchanged. Therefore the derivative of the function y=3x2e2xsin(x) is: dy/dx = 6xe2xsin(x) + 6x2e2xsin(x) + 3x2e2xcos(x).

SR
Answered by Shreya R. Maths tutor

5910 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Differentiate y=x^(-1/2)-x


A factory produces cartons each box has height h and base dimensions 2x, x and surface area A. Given that the capacity of a carton has to be 1030cm^3, (a) Using calculus find the value of x for which A is a minimum. (b) Calculate the minimum value of A.


Two lines have equations r = (1,4,1)+s(-1,2,2) and r = (2,8,2)+t(1,3,5). Show that these lines are skew.


Differentiate sin(x)*x^2


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