Trig + Implicit Differentiation

When we "take the derivative" of a function at a certain point, what are we finding?

• What's a derivative?

• The rate at which our struggles in Calculus are increasing.

• The slope of the secant line.

• The slope of the tangent line at that certain point.

Find dy/dx if y = cos⁵x

• 5cos⁴x

• -5sin⁴x

• 5cos⁴xsinx

• -5cos⁴xsinx

Find the derivative.

• x⁴ cosx - 4x³sinx

• 4x³sinx + x⁴ cosx

• 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 y' if y = tan(3x²+2).

• sec²(3x²+2)

• 6xsec²(3x²+2)

• 6xsec²x(3x²+2)

• sec²(6x)

Find dy/dx if y = sec(8x²).

• sec(16x)tan(16x)

• 16xcos(8x²)

• 16xsecxtanx(8x²)

• 16xsec(8x²)tan(8x²)

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

• 2cos^-1/2(4x)

• 1/2cos^-1/2(4x)

• 2sin^-1/2(4x)cos(4x)

• 1/2sin^-1/2(4x)cos(4x)

Given f (x) = 5sinx + 3x³cosx, f '(x) =

• -5cosx − 3x³sinx + 9x²cosx

• 5sinx − 3x³sinx + 9x²cosx

• 5cosx + 9x²cosx − 3x³sinx

• 5cosx + 3x³sinx + 9x²cosx

Find dy/dx at a given point.

• 5/4

• 4/5

• 1

• -5

• -3
• 8
• 0
• 9