[tex]f(x) = (1 + 3x) \sqrt{x} \\ f '(x) = ((1 + 3x) \sqrt{x}) ' = (1 + 3x) '\sqrt{x} + (1 + 3x) \sqrt{x}' = \\ = ( 1' + (3x)') \sqrt{x} + (1 + 3x) {x}^{ \frac{1}{2}'} \\ = (0 + 3) \sqrt{x} + \frac{1}{2} {x}^{ - \frac {1}{2} } = \\ = 3 \sqrt{x} + \frac{1}{2} \times \frac{1}{ \sqrt{x} } = 3 \sqrt{x} + \frac{1}{2 \sqrt{x} } [/tex]
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[tex]f(x) = (1 + 3x) \sqrt{x} \\ f '(x) = ((1 + 3x) \sqrt{x}) ' = (1 + 3x) '\sqrt{x} + (1 + 3x) \sqrt{x}' = \\ = ( 1' + (3x)') \sqrt{x} + (1 + 3x) {x}^{ \frac{1}{2}'} \\ = (0 + 3) \sqrt{x} + \frac{1}{2} {x}^{ - \frac {1}{2} } = \\ = 3 \sqrt{x} + \frac{1}{2} \times \frac{1}{ \sqrt{x} } = 3 \sqrt{x} + \frac{1}{2 \sqrt{x} } [/tex]