Understanding Derivatives of Common Functions

This video tutorial introduces the derivatives of common functions, focusing on trigonometric, exponential, and logarithmic functions. It explains the derivatives of sine, cosine, and tangent, highlighting their intuitive understanding through graphs. The video also explores the unique property of the exponential function e^x, where its derivative is itself, and discusses the derivative of the natural logarithm, filling a gap left by the power rule. The tutorial serves as a catalog of essential derivatives, setting the stage for future proofs and applications.

What is the derivative of sine of x?

• Negative cosine of x

• Negative sine of x

• Cosine of x

• Sine of x

What is the derivative of cosine of x?

• Negative sine of x

• Negative cosine of x

• Cosine of x

• Sine of x

What is the derivative of tangent of x?

• Cosine squared of x

• Sine squared of x

• Negative secant squared of x

• Secant squared of x

What is unique about the derivative of e^x?

• It is zero

• It is e^x

• It is x

• It is 1

At x = 0, what is the slope of the tangent line for e^x?

• 0

• 1

• e

• x

At x = 1, what is the slope of the tangent line for e^x?

• x

• e

• 1

• 0

Which function's derivative is equal to its own value?

• Natural logarithm

• Exponential function e^x

• Cosine function

• Sine function

What is the derivative of the natural log of x?

• x

• x^2

• 1/x

• ln(x)

Which function's derivative fills the gap left by the power rule for x to the negative 1?

• Cosine function

• Sine function

• Natural logarithm

• Exponential function

What does the power rule not provide a derivative for?

• x^2

• x^3

• x^-1

• x^5