The Differentials: Example 1

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

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

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

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