calculus quick question
posted by dt on .
g(x)= sqrt(14x^2)
Can someone help me find the first and second derivatives please!

write it as
g(x) = (1  4x^2)^(1/2)
g ' (x) = (1/2)(1  4x^2)^(1/2) (8x)
= 4x(1  4x^2)^(1/2)
now by the product rule
g '' (x)
= (4x)(1/2)(14x^2)^(3/2) (8x) 4(1  4x^2)^(1/2)
= (16x^2)(14x^2)^(3/2)  4(1  4x^2)^(1/2)
= 4(1  4x^2)^(3/2) [ 4x^2  (14x^2) ]
= 4(14x^2)^(3/2) (4x^2 + x  2)
= 4( 14x^2)^(3/2)
or
= 4/(1  4x^2)^(3/2)