AP Calculus - Derivative Practice - All Methods

What is the derivative of sin(x)?

• -sin(x)
• -cos(x)
• cos(x)
• sin(x)

When we "take the derivative" of a function 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

What is the derivative of tan(x)?

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

Tags

CCSS.HSF.TF.B.7

Find the derivative.

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

Derive y=(Sin3x)²

• 2Cos(3x)

• 6cos(3x)

• 18xCos(3x)

• 6Cos(3x)Sin(3x)

Find dy/dx  
x³ +y³  = 36

• 6 -x
• 3x² +3y² 
• −x²/y²
• 0

Find dy/dx for
y = 3^2x+5 

• dy/dx = 3^(2x+4)
• dy/dx = (3^(2x+4)) ln 3
• dy/dx = 3^(2x+5) ln3
• dy/dx = (3^(2x+5)) (ln 3) (2)

Tags

CCSS.HSF-IF.C.8B

d/dx (sin²x) = ?

• 2sin x
• 2(sin x)(cos x)
• 2cos x
• 2x(cos x)

Find the derivative:
y=4e^x²

• y'=8xe
• y'=8xe^x²
• y'=8xe^2x
• y'=8xe^4x²

Tags

CCSS.HSF-IF.C.8B

Find the derivative:
y=11^x²

• y′=11^x²(2x)(ln11)
• y′=2x(ln11)
• y′=11^x²(2x)(lnx)
• y′=11^x²(x)(ln11)