Find the derivative of r = 2(1/sqrt theta + sqrt of theta)

Question

i got -1/theta(sq rt of theta) + 2 sq rt of theta howeverrrrr back of the book says 1/theta sq rtof theta + 1/2 sq rt of theta. Pls help and show solution please!

Answer 1

Hi Pia,

r = 2(1/√θ + √θ)

  = 2(θ^-1/2 + θ^1/2 )

dr/dθ = 2(-1/2 θ^-3/2 + 1/2 θ^-1/2)

        =  -θ^-3/2  + θ^-1/2

        = - θ^-1θ^-1/2 + θ^-1/2

        = - 1/(θ√θ) + 1/√θ