Derivatives #2: Trig Derivatives with the Chain Rule

Derivative of cotx

• cosx 
• csc²x
• -csc²x
• cos²x

Derivatve of secx

• sec²x
• secxtanx
• -secxtanx
• tan²x

If a function has a derivative that is negative, what does that tell you?

• The function is increasing
• The function is decreasing

Find the derivative f(x) = (x² + 2x)⁵

• f'(x) = 5(2x+2)⁴
• f'(x) = 5(x² + 2x)⁴
•  f'(x) = 5(x² + 2x)⁴(2x)
• f'(x) = 5(x² + 2x)⁴(2x + 2)

Find the equation of the tangent line at the given point.

• y+1=3(x+1)
• y+1=⅓(x+1)
• y-1=3(x+1)
• y=3x-1

Tags

CCSS.HSA.CED.A.2

CCSS.HSG.GPE.B.5

What is -sinx the derivative of?

• sinx

• -sinx

• cosx

• -cosx

Find dy/dx if y = cos⁵x

• 5cos⁴x
• -5sin⁴x
• 5cos⁴xsinx
• -5cos⁴xsinx

Find y' if y = tan(3x²+2).

• sec²(3x²+2)
• 6xsec²(3x²+2)
• 6xsec²x(3x²+2)
• sec²(6x)

Tags

CCSS.HSF.BF.A.1

CCSS.HSF.IF.A.2

Find f '(x) if f(x) = x⁴sinx

• 4x³cosx
• x⁴cosx
• x⁴cosx + 4x³sinx
• -x⁴cosx + 4x³sinx

Find dy/dx if y = sec(8x²).

• sec(16x)tan(16x)
• 16xcos(8x²)
• 16xsecxtanx(8x²)
• 16xsec(8x²)tan(8x²)