Find the differential dy

Question

let y=tan(5x+6)

Find the differential dy when x=4 and dx=0.4

Find the differential dy when x=4 and dx=0.8

Answer 1

Hi, Dalia!

 

Our first order of business here is to find the derivative of the equation (i.e. differential equation). This requires u-substitution...

 

u = 5x + 6

du = 5 dx

 

Now to the equation...

 

y = tan u

dy = sec²u * du

     = sec²(5x+6)*5dx

 

So now we have our differential equation. Onward...

 

Solve for dy when x = 4 and dx = 0.4...

 

dy = sec²(5*4 + 6)*5*0.4

dy = sec²(26) * 2

dy = 2.38946 * 2

dy = 4.77892

 

Yay! The second case is solved the same way. :)