Trig Differentiation

 $\frac{d}{dx}\left(\frac{\sin x}{1+\cos x}\right)=$  

•  $\frac{\cos x}{-\sin x}$  

•  $\frac{-\sin^2x-\cos x+\cos^2x}{\left(1+\cos x\right)^2}$  

•  $\frac{1}{1+\cos x}$  

•  $\frac{-\cos^2x+\cos x+\sin^2x}{\left(1+\cos x\right)^2}$  

Determine the derivative of:  f(x) = x⁴sinx

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

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 the derivative of f(x) = -3x⁴cscx

• f'(x) = 12x³cscxcotx

• f'(x) = -3x⁴cscxcotx

• f'(x) =-12x³cscx + 3x⁴cotxcscx

• f'(x) = -3xcosx

Find f'(x) if f(x) = sin⁵ x

• 5 sin x

• 5 sin x cos⁴ x

• 5 sin⁴ x cos x

• -5 sin² x cos² x

y = 2tan(1 - 4x)

• -8 sec² (1 - 4x)

• 8 sec² (1 - 4x)

• 2 sec² (1 - 4x)

• 2 sec (1 - 4x)

y = 2 cos⁴ (x-9)

• 8cos³(x-9) sin²(x-9)

• -4cos³(x-9) sin(x-9)

• 8cos³(x-9) sin(x-9)

• -8cos³(x-9) sin(x-9)

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)

Find the derivative of f(x) = -3x⁴cscx

• f'(x) = 12x³cscxcotx

• f'(x) = -3x⁴cscxcotx

• f'(x) =-12x³cscx + 3x⁴cotxcscx

• f'(x) = -3xcosx

 $\frac{\text{d}}{\text{d}x}\left(3\tan^4x\right)$  

•  $12\tan^3x\sec^2x$  

•  $12\tan^3x\sec x$  

•  $12\sec^3x$  

•  $12\sec^6x$