Question

Compute the first three derivatives of f(x)=2x^5+x^(3/5)-1/2x

Answer 1

$$f(x)=2x^5+x^{3/5}-1/2\cdot x^{-1}$$

First derivative:

$$f'(x)=10x^4+3/5\cdot x^{-2/5}+1/2\cdot x^{-2}$$

Second derivative:

$$f''(x)=40x^3-6/25\cdot x^{-7/5}-x^{-3}$$

Third derivative:

$$f'''(x)=120x^2+42/125\cdot x^{-12/5}+3x^{-4}$$