Calculus Derivatives and Trigonometric Functions

The video tutorial explains how to find the value of 'a' in the function f(x) = ax + ln(sin x) such that f'(3π/4) = 3. It begins by deriving the function's derivative, f'(x), and simplifies it to a + cot(x). The tutorial then solves for 'a' by substituting x = 3π/4 and using trigonometric identities to find cot(3π/4). The solution is verified by recalculating the derivative and ensuring it matches the given condition.

What is the function f(x) given in the problem?

• ax + ln(cos(x))

• ax + cos(x)

• ax + ln(sin(x))

• ax + sin(x)

What is the derivative of ax with respect to x?

• 0

• x

• a

• ax

What is the derivative of ln(sin(x)) with respect to x?

• cos(x)/sin(x)

• 1/sin(x)

• sin(x)/cos(x)

• 1/cos(x)

What is the expression for f'(x) after finding the derivatives?

• a + sin(x)

• a + cot(x)

• a + cos(x)

• a + tan(x)

What equation is formed when substituting 3π/4 into f'(x)?

• a + cot(3π/4) = 0

• a + sin(3π/4) = 3

• a + cot(3π/4) = 3

• a + tan(3π/4) = 3

What is the reference angle for 3π/4 in degrees?

• 30 degrees

• 90 degrees

• 45 degrees

• 60 degrees

What is the value of cot(3π/4)?

• 0

• √2

• -1

• 1

What is the value of 'a' that satisfies the equation?

• 2

• 5

• 3

• 4

What is the original function f(x) when a = 4?

• 4x + ln(sin(x))

• 4x + ln(cos(x))

• 4x + cos(x)

• 4x + sin(x)

Does f'(3π/4) equal 3 when a = 4?

• Depends on x

• Cannot be determined

• Yes

• No