# Find the differential of the following function?: y = sin 5x^3

Jun 8, 2018

$\mathrm{dy} = 15 {x}^{2} \cos 5 {x}^{3} \setminus \mathrm{dx}$

#### Explanation:

$y = \sin 5 {x}^{3}$

If you're having trouble, break it down a little. E.g. let:

• $y = \sin z , q \quad z = 5 {x}^{3}$

Which means:

• $\mathrm{dy} = \cos z \setminus \mathrm{dz}$

• $\mathrm{dz} = 15 {x}^{2} \setminus \mathrm{dx}$

So the differential is:

• $\mathrm{dy} = 15 {x}^{2} \cos 5 {x}^{3} \setminus \mathrm{dx}$