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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.

Answer and Explanation: 1

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We can find the derivative of the function as follows.


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

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Applying the Rules of Differentiation to Calculate Derivatives

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Chapter 8 / Lesson 13
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The rules of differentiation are useful to find solutions to standard differential equations. Identify the application of product rule, quotient rule, and chain rule to solving these equations through examples.


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