Question

calcule g '(x) , sendo g dada por 
a) g(x) =4 raiz quadrada de x
b) g(x)= 6 RAIZ quadrada de x
c) g (x) =8 raiz quadrada de x
d) g(x)= 9 raiz quadrada de x

Answer 1

a )

$g(x)=4 \sqrt{x} \\ \\g(x)=4*x^{ \frac{1}{2} }\\ \\g'(x)=4* \frac{1}{2} *x^{ -\frac{1}{2} }\\ \\\boxed{g'(x)= \frac{2}{ \sqrt{x} } }$

b )

$g(x)=6 \sqrt{x} \\g(x)=6*x^{ \frac{1}{2} }\\g'(x)=6* \frac{1}{2} *x^{- \frac{1}{2} }\\ \\\boxed{g'(x)= \frac{3}{ \sqrt{x} } }$

c )

$g(x)=8 \sqrt{x} \\g(x)=8*x^{ \frac{1}{2} }\\g'(x)=8* \frac{1}{2} *x^{- \frac{1}{2} }\\ \\\boxed{g'(x)= \frac{4}{ \sqrt{x} } }$

d )

$g(x)=9 \sqrt{x} \\g(x)=9*x^{ \frac{1}{2} }\\g'(x)=9* \frac{1}{2} *x^{- \frac{1}{2} }\\ \\\boxed{g'(x)= \frac{9}{2 \sqrt{x} } }$