Attempting to identify transitive dependency
Can you get a different answer for subtotal for any specific pair of quantity and price_charged?  No, of course not.  Arithmetic is arithmetic.  

Quantity and price charged depend on invoice_number and line_number, not on product_code at all.  In fact, product_code also depends on invoice_number and line_number. 

EDIT:

Partial Dependencies are dependencies on part of a multi-part key.  Transitive Dependencies are things that depend on non-key attributes.  Step one is to look at your initial relation and determine what the key of the whole thing is, or if there are multiple candidate keys, what they are.

Here are the pieces that I'd guess make up your key, based on the limited sample data and some common sense:


Invoice Number
Line Number


Your table looks to me like an invoice detail table to me.  This means that if you know what invoice and which line on the invoice, you know which distinct record you're looking at.  If that's the case, what do each of the non-key columns depend on?  Let's look at each in turn:


CUTOMER_NUMBER: depends on just the INVOICE_NUMBER, therefore PARTIAL.
PRODUCT_CODE: depends on the whole key, therefore FULL
CUSTOMER_NAME: depends on CUSTOMER_NUMBER (non-key), therefore TRANSITIVE
INVOICE_DATE: depends on just the INVOICE_NUMBER, therefore PARTIAL.
COMMON_NAME: depends on PRODUCT_CODE (non-key), therefore TRANSITIVE.
SCIENTIFIC_NAME and CATEGORY (ditto)
QUANTITY: depends on the whole key, therefore FULL.
PRICE_CHARGED: depends on PRODUCT_CODE (non-key), therefore TRANSITIVE.


As noted previously, SUBTOTAL is calculated based on QUANTITY and PRICE_CHARGED so it depends on the full key as well.