If h(x) = 2xsin(2x), find h'(x).

Differentiate using product rule as expression consist of two functions.Product Rule: d(f(x)g(x))/dx = g(x).f'(x) + f(x).g'(x)Chain Rule: d(f(g(x)))/dx = g'(x) . f'(g(x))
Let: f(x) = 2x f'(x) = 2 - simple differentiation g(x) = sin(2x) g'(x) = 2cos(2x) - chain rule as function is composite
Therefore: h'(x) = sin(2x).2 + 2x.2cos(2x)
Final Answer: h'(x) = 2sin(2x) + 2xcos(2x)

Answered by Meer S. Maths tutor

3406 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Differentiate y = 2x^3 + 6x^2 + 4x + 3 with respect to x.


The curve C has equation (4x^2-y^3+3^2x)=0. The point P (0,1) lies on C: what is the value of dy/dx at P?


How can the cosine rule be derived?


For sketching the graph of the modulus of f(x) (in graph transformations), why do we reflect in the x-axis anything that is below it?


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