Find dy/dx for y = x^3*e^x*cos(x)

In this problem, we see that y is a product of 3 functions of x. That means that in order to find dy/dx we need to use the product rule. The product rule tells us that in this case we should differentiate one function at a time, keeping the others unchanged. That would mean that we will end with 3 terms - one for each function that we differentiate - multiplied by the other 2. So the solution here will be: firstly: d(x3 )/dx= 3x2 secondly: d(ex)/dx = ex thirdly: d(cos(x))/dx = -sin(x) and so the solution is: dy/dx = 3*x2*ex*cos(x) + x3*ex*cos(x) + x3ex(-sin(x))

LN
Answered by Lyudmil N. Maths tutor

9664 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

The cubic polynomial f(x) is defined by f(x) = 2x^3 -7x^2 +2x+3. Express f(x) in a fully factorised form.


Simplify fully: (5 +√7)/ (2+√7)


Express x^2+3x+2 in the form (x+p)^2+q, where p and q are rational numbers.


Find the set of values of k for which x^2 + 2x+11 = k(2x-1)


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences