Derivatives and Chain Rule Concepts

The video tutorial explains how to find the derivatives of composite functions. It begins with the function f(x) = tan(sin(-3x)), using the chain rule to differentiate the outer tangent function and the inner sine function. The process involves identifying the inner function and its derivative, then applying the derivative formula for tangent. The tutorial then moves to the function g(x) = cos(cot(2x)), again using the chain rule to differentiate the outer cosine function and the inner cotangent function. The video emphasizes the importance of understanding the composition of functions and applying the chain rule effectively.

What is the outer function in the composite function f(x) = tangent of sine of negative three x?

• Sine

• Tangent

• Negative three x

• Secant

Which rule is primarily used to find the derivative of f(x) = tangent of sine of negative three x?

• Product Rule

• Quotient Rule

• Chain Rule

• Power Rule

What is the derivative of sine of negative three x with respect to x?

• Three cosine of negative three x

• Negative sine of negative three x

• Negative three cosine of negative three x

• Cosine of negative three x

What is the final expression for f'(x) after applying the chain rule?

• Negative three secant squared of sine of negative three x times cosine of negative three x

• Secant squared of sine of negative three x times sine of negative three x

• Three secant squared of sine of negative three x times cosine of negative three x

• Negative secant squared of sine of negative three x times cosine of negative three x

What is the derivative of tangent u with respect to x?

• Sine u times u prime

• Secant squared u times u prime

• Negative secant squared u times u prime

• Negative sine u times u prime

What is the inner function in g(x) = cosine of cotangent of two x?

• Two x

• Cotangent of two x

• Sine

• Cosine

Which formula is used to find the derivative of cosine u with respect to x?

• Cosine u times u prime

• Negative cosine u times u prime

• Sine u times u prime

• Negative sine u times u prime

What is the derivative of cotangent of two x with respect to x?

• Sine of two x times two

• Negative sine of two x times two

• Cosecant squared of two x times two

• Negative cosecant squared of two x times two

What is the final expression for g'(x) after simplifying?

• Positive two sine of cotangent two x times cosecant squared of two x

• Negative two sine of cotangent two x times cosecant squared of two x

• Two cosine of cotangent two x times cosecant squared of two x

• Negative cosine of cotangent two x times cosecant squared of two x

What is the derivative of cosine u with respect to x?

• Cosine u times u prime

• Negative sine u times u prime

• Sine u times u prime

• Negative cosine u times u prime