The Differentials: Example 1

Problem:

Find dy if y=x^3-4x^2+5x.

Solution:

We get the differential of both sides of the equation.

dy=d\left(x^3-4x^2+5x\right)

We apply the different differential formulas

dy=d\left(x^3\right)+d\left(-4x^2\right)+d\left(5x\right)

dy=3x^2\:dx-8x\:dx+5\:dx

dy=\left(3x^2-8x+5\right)dx