10) Demonstrate and explain how to find the derivative of the following function. Be sure to explicity denote which derivative rules your ane using a) $$ f(y)=7 y^{6}-6 y^{5}+5 y+6 $$ a

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We need to differentiate the function

f(y) = 7y⁶ – 6y⁵ + 5y + 6

To do this, we will use these derivative rules:

1. Power Rule: If f(y) = yⁿ, then f '(y) = n·yⁿ⁻¹.
2. Constant Multiple Rule: If f(y) = c·g(y), then f '(y) = c·g '(y).
3. Sum/Difference Rule: The derivative of a sum or difference is the sum or difference of the derivatives.

Step-by-Step Differentiation:

1. Differentiate 7y⁶:
  Using the constant multiple rule combined with the power rule,
    d/dy (7y⁶) = 7 * d/dy (y⁶) = 7 * (6y⁵) = 42y⁵.

2. Differentiate –6y⁵:
  Similarly,
    d/dy (–6y⁵) = –6 * d/dy (y⁵) = –6 * (5y⁴) = –30y⁴.

3. Differentiate 5y:
  Again using the constant multiple rule and knowing that the derivative of y is 1,
    d/dy (5y) = 5 * (d/dy y) = 5 * 1 = 5.

4. Differentiate 6:
  The derivative of a constant is zero,
    d/dy (6) = 0.

Now, combine these results to get the overall derivative:
  f '(y) = 42y⁵ – 30y⁴ + 5 + 0

Thus, the final derivative is:
  f '(y) = 42y⁵ – 30y⁴ + 5

This concludes the differentiation of the function, using the power, constant multiple, and sum/difference rules explicitly.
The derivative of $$ f(y) = 7y^{6} - 6y^{5} + 5y + 6 $$ is $$ f '(y) = 42y^{5} - 30y^{4} + 5 $$.

10) Demonstrate and explain how to find the derivative of the following function. Be sure to explicity denote which derivative rules your ane using a) \( f(y)=7 y^{6}-6 y^{5}+5 y+6 \) a

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