Calculus: Derivatives and Rules

This video tutorial covers the application of the product and quotient rules to trigonometric functions. It reviews the derivatives of sine and cosine and introduces the derivatives of tangent, cotangent, secant, and cosecant. The video includes a proof of the derivative of tangent using the quotient rule and provides several example problems to demonstrate the application of these rules. It also discusses techniques for simplifying derivatives and avoiding the quotient rule when possible.

What is the primary focus of this video tutorial?

• Introduction to calculus

• Algebraic expressions

• Product and quotient rules with trigonometric functions

• Integration techniques

Which derivative is equal to secant squared x?

• Derivative of tangent x

• Derivative of cosine x

• Derivative of sine x

• Derivative of cotangent x

How can the derivative of tangent x be expressed using sine and cosine?

• sin x / cos x

• cos x / sin x

• cos x + sin x

• sin x * cos x

What is the derivative of y = cose x - 4 sin x?

• 2 cose x - 4 sin x

• -2 cose x - 4 sin x

• -2 cose x + 4 sin x

• 2 cose x + 4 sin x

When applying the product rule, what is the first step?

• Add the derivatives of both functions

• Multiply the first function by the derivative of the second

• Find the derivative of the second function

• Subtract the derivative of the first from the second

In the expression x^2 times secant x, what common factor can be factored out?

• x

• secant x

• x^2

• tangent x

What is the derivative of y = x * secant x + tangent x using the product rule?

• secant x + x tangent x

• x tangent x + secant x

• x secant x + tangent x

• x secant x tangent x + secant x

What is the first step in applying the quotient rule?

• Square the denominator

• Multiply the denominator by the derivative of the numerator

• Subtract the numerator from the denominator

• Square the numerator

How can you simplify the expression 1 / sin^2 x?

• Add sin x

• Divide by sin x

• Multiply by sin x

• Multiply by the reciprocal

What is the derivative of tangent x?

• Cosecant squared x

• Cosecant x

• Secant squared x

• Secant x