The Differentials: Example 3

Problem:

Find d\left(\frac{1}{\sqrt{x^3+7}}+4x^2-1\right).

Solution:

=d\left(\frac{1}{\sqrt{x^3+7}}\right)+d\left(4x^2\right)+d\left(-1\right)

=\left(-\frac{3x^2}{2\left(\sqrt{x^3+7}\right)^3}+8x\right)dx