Question

Find y'', if y = x² + \(\rm 3x^{1\over2}\)- \(\rm 5x^{2\over5}\).
1. y'' = 2 + \(3\over4\)x\(-{3\over2}\) - \(6\over 5\)x\(-{8\over5}\) 
2. y'' = 2 - \(3\over4\)x\(-{3\over2}\) - \(6\over 5\)x\(-{8\over5}\) 
3. y'' = 2 - \(3\over4\)x\(-{3\over2}\) + \(6\over 5\)x\(-{8\over5}\) 
4. y'' = 2 + \(3\over4\)x\(-{3\over2}\) + \(6\over 5\)x\(-{8\over5}\) 
5. None of these

Answer 1

Correct Answer - Option 3 : y'' = 2 - \(3\over4\)x\(-{3\over2}\) + \(6\over 5\)x\(-{8\over5}\) 

Concept:

• \(\rm d\over dx\)xn = nxn-1

Calculation:

Given y =  x2 + \(\rm 3x^{1\over2}\)- \(\rm 5x^{2\over5}\)

Differentiating with respect to x 

y' = 2x + 3(\(\rm 1\over 2\)x\(^-{1\over2}\)) - 5(\(2\over 5\)x\(^-{3\over5}\))

y' = 2x + \(3\over2\)x\(-{1\over2}\) - 2x\(-{3\over5}\) 

Differentiating again with respect to x

y'' = 2 + \(3\over2\)(\(-{1\over2}\)x\(-{3\over2}\)) - 2(\(-{3\over5}\)x\(^-{8\over5}\))

y'' = 2 - \(3\over4\)x\(-{3\over2}\) + \(6\over 5\)x\(-{8\over5}\)