Given that y=(4x+1)^3*sin(2x) , find dy/dx

y=(4x+1)^3*sin(2x) - this is a product of two functions of x. It can be rewritten as y = u(x)*v(x)   ; where u(x) = (4x+1)^3 and v(x) = sin(2x)

Using the product rule: dy/dx = u'(x)*v(x) + v'(x)*u(x) where the ' (prime) notation denotes the differential with respect to x

u'(x) = 34(4x+1)^2   and  v'(x) = 2*cos(2x)   using either substitution or simplification rules for both

Therefore, using product rule, dy/dx=[ 34(4x+1)^2 ] * [ sin(2x) ]  +  [ 2*cos(2x) ] * [ (4x+1)^3 ] 

which simplifies to: dy/dx = 2(4x+1)^3*cos(2x) + 12(4x+1)^2

Answered by Chris D. Maths tutor

2305 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Solve, giving your answer to 3 s.f. : 2^(2x) - 6(2^(x) ) + 5 = 0


How do I find the cartesian equation for a curve written in parametric form?


x is an angle, if 180 > x > 90 and sinx = √2 / 4 what is the value of angle x


How do I solve a simultaneous equation in two variables when they have with different coefficients?


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 2013–2024

Terms & Conditions|Privacy Policy