Functions and Their Derivatives

Determine the derivative of:  f(x) = x⁴sinx

• x⁴ cosx - 4x³sinx
• x⁴ cosx + 4x³sinx
• 4x³cosx
• -4x³cosx

Find the derivative f(x) = tanxcosx

• f'(x) = sec²xcosx - tanxsinx
• f'(x) = sec²xcosx + tanxsinx
• f'(x) = sec²xsinx
• f'(x) = sec²xcosx - tanxcosx

If f(x) = sin³(2x), then f'(x) =

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

What is the derivative of -cos(x)?

• sin(x)
• -sin(x)
• cos(x)
• -cos(x)

What is the derivative of cot(x)?

• sec²(x)
• -sec²(x)
• csc²(x)
• -csc²(x)

What is the derivative of tan(x)?

• -sec²(x)
• -csc²(x)
• sec²(x)
• csc²(x)

What is f'(x) if f(x) = cos(5x⁴)?

• f'(x) = sin(20x³)
• f'(x) = 20x³ sin(5x⁴)
• f'(x) = -sin(20x³)
• f'(x) = -20x³ sin(5x⁴)

Find g'(x) if g(x) = sin^1/2(4x)

• 2cos^-1/2(4x)
• 4cos^1/2(4x)
• 2sin^-1/2(4x)cos(4x)
• 1/2sin^-1/2(4x)cos(4x)

If f(x) = -csc(x/2), then f'(x) =

• sec²(x/2)

• 2csc(x/2)cot(x/2)

• ½csc(x/2)cot(x/2)

• -csc²(x/2)

y= sin²x find y'

• 2sin x

• 2(sin x)(cos x)

• 2cos x

• 2x(cos x)