Question

Find the differential of the function

a. y=x4sin(9x)
b. y=x4sin⁡(9x).

Answer 1

We want to find:

`y'*dx = dy`

Where:

`y = x^4*sin(9x)`

Remember that when we have a function like:

f(x) = g(x)*h(x)

The derivation gives:

f'(x) = g'(x)*h(x) + g(x)*h'(x)

In this case we can define:

f(x) = y

g(x) = x^4

h(x) = sin(9x)

These functions are easy to differentiate:

g'(x) = 4*x^3

h'(x) = 9*cos(9*x)

Then we have:

`y' = (dy)/(dx) = 4x^3*sin(9x) + x^4*9cos(9x)`

Then we can write:

`dy = (4x^3*sin(9x) + 9x^4*cos(9x))dx`