Understanding Derivatives and Differentiation

The video tutorial explains how to find the derivative of a function using differentiation formulas. It introduces the variables and constants involved, derives U Prime, and calculates the final derivative. The tutorial concludes with the final result, providing a clear understanding of the process.

What is the initial function for which we need to find the derivative?

• f(x) = 6 * 5^x

• f(x) = 6 * x^5

• f(x) = 5 * x^6

• f(x) = 5 * 6^x

What is the value of 'a' in the differentiation formula used?

• 5

• 12

• 6

• x

How is U' (U prime) expressed in terms of x?

• 12x^2

• 12x^-2

• 1/2x

• x^12

What is the simplified form of the derivative of the function?

• 3 * 5^x

• 6 * 5^x

• 6 * natural log 5 * 5^x

• 3 * natural log 5 * 5^x

What is the final result of the derivative expressed as?

• FR Prime of x = 3 * natural log 5 * 5^x

• FR Prime of x = 6 * natural log 5 * 5^x

• FR Prime of x = 6 * 5^x

• FR Prime of x = 3 * 5^x