Question

A derivada da função f(y) = In (y) / raiz y é dada por quanto?

Answer 1

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$\sf f(y)=\dfrac{\ell n(y)}{\sqrt{y}}=\ell n(y)\cdot y^{-\frac{1}{2}}\\\sf f'(y)=\dfrac{1}{y}\cdot y^{-\frac{1}{2}}+\ell n(y)\cdot\left(-\dfrac{1}{2}\right)y^{-\frac{3}{2}}\\\sf f'(y)=\dfrac{1}{y\cdot y^{\frac{3}{2}}}-\dfrac{1}{2y^{\frac{3}{2}}}\\\sf f'(y)=\dfrac{1}{y^{\frac{3}{2}}}-\dfrac{1}{2y^{\frac{3}{2}}}\\\sf f'(y)=\dfrac{2-1}{2y^{\frac{3}{2}}}\\\sf f'(y)=\dfrac{1}{2y^{\frac{3}{2}}}$

$\huge\boxed{\boxed{\boxed{\boxed{\sf f'(y)=\dfrac{1}{2\sf{\sqrt[\sf 3]{\sf y}}}}}}}$