If h(θ) = θ cos θ , find h'(θ) and h''(θ).

Solution:

Given if h(θ) = θ cos θ

Consider θ as a variable and differentiate w.r.t θ

Using the product rule :

h'(θ) = cosθ * 1 + θ * (-sin θ)

h’(θ) = cosθ - θsinθ — (a)

h’’(θ) = -sinθ - {sinθ*1 + θcosθ}

h’’(θ) = -sinθ - sinθ - θcosθ

h’’(θ) = -2sinθ - θcosθ — (b)

If h(θ) = θ cos θ , find h'(θ) and h''(θ).

Summary:

If h(θ) = θ cos θ, then h'(θ) = cosθ - θsinθ and h''(θ) = -2sinθ - θcosθ.