How Do You Correctly Apply the Product and Quotient Rules in Differentiation?

[DBeckett91]

I have 2 separate equations that I have to finish, but my lecturer is extremely slow at marking and I need to get it marked off asap, so if you could give me a hand it would be hugely appreciated.

For all of these equations I need to differentiate with respect to the variable and give the final simplified answers.

Equation 1: y = 8sin(125t)e^-7t
The value of t is unknown

The rule I was using is u(dv/dx) + v(du/dx)

y=8sin(125t)e^-7t

u = 8sin(125t)
v = e^-7t

Answer = 8sin(125t) (7e^-7t/dx) + 7e^-7t(8sin(125t)/dx)

Equation 2: s = (8x^2-7x +125)/8x+7

The rule I used was (v(du/dx) - u(dv/dx)/v^2)

s = (8x^2-7x +125)/8x+7

u = 8x^2-7x +125
= 16x - 7

v = 8x + 7
= 8

ds/dx = (8(16x-7/dx) - 16x-7(8/dx))/64

 

[hunt_mat]

I assume that you're differentiating right? Then you're writing is wrong, you should write:

$$\frac{du}{dt}=8\times 125\cos (125t),\quad\frac{dv}{dt}=-7e^{-7t}$$

So the product rule you should be using is d(uv)/dt=vdu/dt+udv/dt, there are no x's around. That is where you made your error.