[tex]f(x) = 3{x}^{5} - \frac{4}{ {x}^{4} } + 2 \sqrt{x} .[/tex]
[tex]f'(x) = (3 {x}^{5} )' - ( \frac{4}{ {x}^{4} } )' + (2 \sqrt{x} )' = 3 ( {x}^{5} )' - 4( \frac{1}{ {x}^{4} } )' + 2( \sqrt{x} )' = 3 \times 5 \times {x}^{4} - 4( {x}^{ - 4} ) + 2 \times \frac{1}{2 \sqrt{x} } = 15 {x}^{4} - 4 \times ( - 4) \times {x}^{ - 5} + \frac{2}{2 \sqrt{x} } = 15 {x}^{4} + 16 {x}^{ - 5} + \frac{1}{ \sqrt{x} } [/tex]
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[tex]f(x) = 3{x}^{5} - \frac{4}{ {x}^{4} } + 2 \sqrt{x} .[/tex]
[tex]f'(x) = (3 {x}^{5} )' - ( \frac{4}{ {x}^{4} } )' + (2 \sqrt{x} )' = 3 ( {x}^{5} )' - 4( \frac{1}{ {x}^{4} } )' + 2( \sqrt{x} )' = 3 \times 5 \times {x}^{4} - 4( {x}^{ - 4} ) + 2 \times \frac{1}{2 \sqrt{x} } = 15 {x}^{4} - 4 \times ( - 4) \times {x}^{ - 5} + \frac{2}{2 \sqrt{x} } = 15 {x}^{4} + 16 {x}^{ - 5} + \frac{1}{ \sqrt{x} } [/tex]