Differentiate the function f(x) = 2x^3 + (cos(x))^2 + e^x

When differentiating a function that is the sum of three different parts we can differentiate each part separately:

a) 2x3 is easy to differentiate. We remember the rule d/dx[axb] = abxb-1. So

2x3 --> 6x2

b) (cos(x))2 is a bit harder. We can use the chain rule, as we have a function raised to a power. The chain rule is:

d/dx[(g(x))n] = n(g(x))n-1 * d/dx[g(x)]

Also we need to remember that cos(x) differentiates to -sin(x)

So we have that

(cos(x))2 --> -2cos(x)sin(x).

c) ex is the easiest of the lot: it doesnt change when differentiated. 

ex --> ex

Therefore the final answer is:

d/dx[f(x)] = 6x2 - 2cos(x)sin(x) + ex

SP
Answered by Seth P. Maths tutor

5418 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

There's a school in India where only 60% of students have internet access. What is the probability of choosing eight students randomly, five of whom have internet access? (Info: Each student's internet access (or lack of it) is independent from all others


Show how '2sin(x)+sec(x+ π/6)=0' can be expressed as √3sin(x)cos(x)+cos^2(x)=0.


In the triangle ABC, AB = 16 cm, AC = 13 cm, angle ABC = 50 and angle BCA= x Find the two possible values for x, giving your answers to one decimal place.


When using the addition rule in probability, why must we subtract the "intersection" to find the "union" with the Addition Rule?


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