Understanding Derivatives of Exponential Functions

The video tutorial explains how to determine the derivative of an exponential function using the chain rule. It begins by identifying the composite function and its inner function, then applies the chain rule to find the derivative. The process involves rewriting the function in terms of 'u' and calculating the derivative using the natural logarithm. The tutorial concludes with a simplified expression of the derivative and a preview of the next video, which will cover the product rule.

What is the first step in finding the derivative of a composite exponential function?

• Identify the base of the exponential function.

• Determine the inner function.

• Apply the product rule.

• Use the power rule.

What is the inner function in the given problem?

• Natural log of 7.

• 4x.

• 7 to the power of x.

• 2x squared plus 3.

Which rule is applied to differentiate the composite function?

• Chain rule.

• Product rule.

• Power rule.

• Quotient rule.

What is the derivative of the inner function, 2x squared plus 3?

• 8x.

• 6x.

• 4x.

• 2x.

How is the derivative of 7 to the power of the inner function expressed?

• Natural log of 7 times 7 to the power of the inner function.

• 7 times the inner function.

• 7 to the power of x.

• Natural log of the inner function.

What is the final expression for the derivative of the function?

• 6x natural log 7 times 7 to the power of 2x squared plus 3.

• 2x natural log 7 times 7 to the power of 2x squared plus 3.

• 8x natural log 7 times 7 to the power of 2x squared plus 3.

• 4x natural log 7 times 7 to the power of 2x squared plus 3.

What topic will be covered in the next video?

• The chain rule.

• The quotient rule.

• The product rule and derivative of an exponential function.

• The power rule.