Question

Am nevoie de ajutor la derivate. Cat face?

Answer 1

$f={x}^{2}$

$g=\sqrt{x}$

$( {x}^{2} \sqrt{x} )' = ( {x}^{2} )' \times \sqrt{x} + {x}^{2} \times ( \sqrt{x} )'$

$= 2 {x}^{2 - 1} \times \sqrt{x} + {x}^{2} \times \frac{1}{2 \sqrt{x} }$

$= 2x \sqrt{x} + \frac{ {x}^{2} }{2 \sqrt{x} } = \frac{ {(2 \sqrt{x}) }^{2} \times x + {x}^{2} }{2 \sqrt{x} }$

$= \frac{ {2}^{2} \times {( \sqrt{x} )}^{2} \times x + {x}^{2} }{2 \sqrt{x} } = \frac{4 {x }^{2} + {x}^{2} }{2 \sqrt{x} } = \frac{5 {x}^{2} }{2 \sqrt{x} }$

$=\frac{5{x}^{2}}{2{x}^{\frac{1}{2}}}=\frac{5{x}^{2-\frac{1}{2}}}{2}=\frac{5{x}^{\frac{3}{2}}}{2}$

Formulă :

$(f \times g)'=f' \times g+f \times g'$