Use the chain rule to find dy/dx, and express the answer in terms of x.?

Question

y=3u^2+2u, u=4x

Answer 1

y= 3(4x)^2+2(4x)

y= 48x^2+8x

dy/dx = 96x+8

or you can take derivative separate

y= 3u^2+2u

dy/du = 6u +2

u= 4x

du/dx =4

but dy/dx = (dy/du)(du/dx) = (6u+2)4 = (6*4x+2)4
= (24x+2)4 = 96x+8

Answer 2

y = 3u^2 + 2u

dy = 6u du + 2 du

but u = 4x and

du = 4 dx

substituting these in dy

dy = 6(4x) (4)dx + 2 (4) dx

dy = 96 x dx + 8dx

dy/dx = 96x + 8

Answer 3

dy/dx = 2(3u) + 2

= 6u + 2

= 24x + 2

= 2( 12x +1 )


smile!

Answer 4

dy/dx = dy/du*du/dx =(6u+2)*(4) = 96x+8

Answer 5

dy/du = 6u+2

du/dx =4

dy/dx= (dy/du)*(du/dx)
dy/dx=(6u+2)*4
as u want in terms of x

substitue u=4x in dy/dx
dy/dx = {6(4x)+2}*4
dy/dx={24x+2}*4
dy/dx=96x+8

Answer 6

y = a million - e^(-t) get dy/dt dy/dt = 0 - (-a million)e^(-t) dy/dt = e^(-t) x = t + e^(-t) get dx/dt dx/dt = a million - e^(-t) to get dy/dx, divide dy/dt via dx/dt: dy/dx = e^(-t)/(a million-e^(-t)) simplify via multiplying the numerator and denominator via e^(t) dy/dx = a million/(e^(t)-a million)