Differentiation of Trigonometric Functions

This video tutorial introduces derivatives, emphasizing the importance of practice. It covers the application of the chain and product rules to find derivatives of various functions, including trigonometric and exponential functions. The tutorial also demonstrates simplifying derivatives using the product rule instead of the quotient rule and concludes with an example involving trigonometric identities.

What is the derivative of the inside function in the example f(x) = sin(3x^5 + 2x)?

• 15x^4 + 2

• 3x^5 + 2

• 5x^4 + 3

• 3x^4 + 5

In the function y = e^x * cos^5(x), what is the derivative of e^x?

• x^4

• 5e^(x-1)

• x * e^(x-1)

• e^x

When differentiating y = e^x * cos^5(x), what rule is applied to the term cos^5(x)?

• Sum Rule

• Power Rule

• Quotient Rule

• Chain Rule

What is the derivative of ln(x) in the function ln(x) / (3x + 10)?

• x

• ln(x)

• 1/x

• 3x + 10

In the function ln(x) / (3x + 10), what is the derivative of the denominator 3x + 10?

• 3x

• 10

• 3

• 1

What is the simplified form of the derivative of sin(x) / cos(x)?

• 1

• tan(x)

• sin^2(x)

• sec^2(x)

In the differentiation of sin(x) / cos(x), what trigonometric identity is used?

• tan(x) = sin(x) / cos(x)

• sin^2(x) + cos^2(x) = 1

• cos^2(x) = 1 - sin^2(x)

• sec^2(x) = 1 + tan^2(x)

What is the derivative of cos(x) in the function sin(x) / cos(x)?

• -sin(x)

• cos(x)

• tan(x)

• sec(x)

Which rule is primarily used to differentiate the function sin(x) / cos(x)?

• Power Rule

• Chain Rule

• Product Rule

• Quotient Rule

What is the result of differentiating the function sin(x) / cos(x) using the product and chain rules?

• 1

• sec^2(x)

• tan(x)

• cos^2(x)