Differentiation and Derivatives Quiz

Differentiate y=sin(2x)

• 2sin2xcosx

• 2sinxcosx (Correct)

• sinxcosx

• sinx

Evaluate dx/d(p x)

• pxi

• xp x−1

• p x lnp (Correct)

• lnp

Evaluate dE/d(tan−1 E)

• 1+E2 1 (Correct)

• 1−E2 1

• 1

• 1+E2 −1

Evaluate dx/d(cosx) at x=2π

• 0

• 1

• -1 (Correct)

• 90

Find the differential coefficient of sin(logx) with respect to x

• −cos(logx) (Correct)

• cos(logx)

• xsin(logx)

• logx

If x=x(t) and y=y(t) are parametric functions, what is dx/dy?

• x(t)2y(t)

• x′(t)y′(t) (Correct)

• x′(t)y′(t)

• x(t)y(t)

Differentiate y=cos−1 a

• 1−a2 1

• 1−a2 1 (Correct)

• 1+a2 1

• 1+a2 1

Obtain dΩ/d(secΩ)

• secΩcotΩ

• cosΩ

• secΩtanΩ (Correct)

• sec2Ω

Differentiate y=sin−1 a

• 1−x2 1

• 1−a2 1 (Correct)

• 1+a2 −1

• 1+a2 1

Which rule of differentiation is most important and widely used?

• Chain rule (Correct)

• Product rule

• Chain production

• Chain control