Question

Derivada $f(x)= \frac{ 7x^{2} }{2( \sqrt[5]{3x+1} } + \sqrt{3x+1}$

Answer 1

$f(x)= \dfrac{7x^2}{2. \sqrt[5]{3x+1} } + \sqrt{3x+1}\\\\\\f(x)= \dfrac{7}{2}.x^2.( 3x+1)^{- \frac{1}{5}}+(3x+1)^{ \frac{1}{2} }\\\\\\f'(x)= \dfrac{7}{2}.2x.(3x+1)^{ -\frac{1}{5} }+ \dfrac{7}{2}.x^2.( -\dfrac{3}{5}).(3x+1)^{ -\frac{6}{5} }+ \dfrac{3}{2}.(3x+1)^{ -\frac{1}{2} }\\\\\\f'(x)= \dfrac{7x}{ \sqrt[5]{3x+1} }- \dfrac{21x^2}{10 \sqrt[5]{(3x+1)^6} }+ \dfrac{3}{2 \sqrt{3x+1} }\\\\\\f'(x)=\dfrac{7x}{ \sqrt[5]{3x+1} }- \dfrac{21x^2}{10.(3x+1). \sqrt[5]{(3x+1)} }+ \dfrac{3}{2 \sqrt{3x+1} }$