Implicit differentiation using the chain and product rule with cosine

The video tutorial explains the application of the chain rule in calculus, focusing on differentiating composite functions. It begins by identifying the outer and inner functions, using cosine and XY as examples. The tutorial then demonstrates how to find the derivative of the inner function XY with respect to X, incorporating implicit differentiation. Next, it covers the derivative of the outer function, cosine, and how to combine these derivatives using the chain rule. The tutorial concludes by emphasizing the importance of understanding both the chain rule and product rule in calculus.

What is identified as the outer function in the chain rule example?

• Sine of X

• Cosine of X

• Tangent of X

• Exponential of X

In the context of the chain rule, what is the inner function labeled as?

• W

• V

• Z

• U

What is the derivative of the inner function XY with respect to X?

• 1 * Y * X

• 1 * X + 1 * Y

• 1 * Y + X * DY/DX

• 1 * X * DY/DX

What is the derivative of cosine of U in the chain rule?

• Positive sine of U

• Negative cosine of U

• Negative sine of U

• Positive cosine of U

What must be multiplied by the derivative of the outer function in the chain rule?

• The original function

• The derivative of the inner function

• The integral of the inner function

• The square of the inner function