# Find the first derivative of the following function: {eq}Y = 5X^{4/5} + 3X^3 - 2X^{3/2} - 10 {/eq}

## Question:

Find the first derivative of the following function: {eq}Y = 5X^{4/5} + 3X^3 - 2X^{3/2} - 10 {/eq}

## Differentiation:

The first derivative of a product can be found by differentiating it once. This derivative gives us the change in the value of the function when its input increases by 1 unit.

\begin{align} Y'& = \frac{\mathrm{d} }{\mathrm{d} X}\left ( 5X^{4/5} + 3X^3 - 2X^{3/2} -...