Differentiate y = 7(x)^2 + cos(x)sin(x)

This question uses a combination of standard differentiation and the product rule. The second part of the equation cos(x)sin(x) is the product of two funtions so the product rule must be used. Product rule: (fg)'(x) = f '(x)g(x) + f(x)g'(x) Let f(x) = cos(x) and g(x) = sin(x). The differentials are: f'(x) = -sin(x) and g'(x) = cos(x)

Differentiating the equation you get dy/dx = 14x + -sin(x)sin(x) + cos(x)cos(x)  dy/dx = 14x + cos^2(x) - sin^2(x) The equation is now differentated but can be simplified by using the identity cos(2x) = cos^2(x) - sin^2(x) The final answer is therfore: dy/dx = 14x + cos(2x)

EC
Answered by Edward C. Maths tutor

3350 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

The functions f and g are defined by f : x → 2x + ln 2, g : x → e^(2x). Find the composite function gf, sketch its graph and find its range.


What is the best way to revise for a Maths A-level?


The curve y = 2x^3 -ax^2 +8x+2 passes through the point B where x = 4. Given that B is a stationary point of the curve, find the value of the constant a.


How do I find and determine the nature of stationary points of a function?


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