Determine the derivative of the following implicit functionsShow your complete and detailed solutions.

Implicit Differentiation

1. 3x² - 5y⁶ = 2x

2. 2x + 9y = 6x²y - 5x³

3. (2x - 9y)² +7y =27x

4. ³ 3x - y + 6x⁴y² = 9y

5. ⁴(7x - 7y)³ - 2y² = 8x

Determine the derivative of the following functions.

Differentiation of Exponential and Logarithmic Functions

1. y = e^9x-5

2. y = 2x ln (x+2)

3. y = (2x - 5) log (3x² - 6x)

4. y = (4x - 5) e^{x^2 - 2x + 1}

5. y = a^{(10x^2 - 8x + 7)}