Learn how to take the derivative using the chain rule twice with cosine

The video tutorial explains the application of the chain rule in calculus, focusing on differentiating composite functions. It begins with an introduction to the chain rule, followed by identifying and differentiating parent functions. The tutorial then covers applying the chain rule to inner functions and combining derivatives of parent and child functions. Finally, it formulates the final derivative expression, emphasizing careful calculation to avoid errors.

What is the primary focus when dealing with a nested chain rule?

• Identifying the largest 'parent' function first

• Ignoring the chain rule

• Identifying the smallest function first

• Differentiating the innermost function first

What is the derivative of X^3 with respect to X?

• X^3

• X^2

• 3X^2

• 3X

When applying the chain rule to cosine of X^2, what is the derivative of cosine?

• Tangent

• Sine

• Negative cosine

• Negative sine

What is the derivative of X^2 with respect to X?

• 2X

• X

• X^2

• 2

What is the final expression for DY over DX in the given function?

• -6X times cosine of X^2 squared times sine of X^2

• -6X times cosine of X^2 times sine of X^2

• -6X times sine of X^2

• 6X times cosine of X^2