Derivatives of Trig Functions

If f(x) = sin³(2x), then f'(x) =

• 3cos(2x)
• 3sin(2x)⋅2
• 3sin²(2x)cos(2x)
• 6sin²(2x)cos(2x)

What is the derivative of -cos(x)?

• sin(x)
• -sin(x)
• cos(x)
• -cos(x)

What is the derivative of -sin(x)?

• -sin(x)
• -cos(x)
• cos(x)
• sin(x)

If f(x)=1/2csc(2x)

• -csc(2x)cot(2x)
• -4csc(2x)cot(2x)
• -csc²(2x)
• 4sec(2x)

If f(x) = sec(4x), then f'(x) =

• 4sec(4x)tan(4x)
• 2sec(4x)tan(4x)
• -4csc(4x)cot(4x)
• -2csc(4x)cot(4x)

If f(x) = 4tan(½-x), then f'(x) =

• 4sec²(1/2 -x)
• -4csc²(1/2 - x)
• -4sec²(1/2-x)
• 4csc²(1/2-x)

If f(x) = -csc(x/2), then f'(x) = 

• sec²(x/2)
• 2csc(x/2)tan(x/2)
• ½csc(x/2)tan(x/2)
• -csc²(x/2)