calculus quick question
posted by dt .
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)
Respond to this Question
Similar Questions

math,algebra,help
Directions are simplify by combining like terms. x radiacal 18 3 radical 8x^2 can someone show me how to do these types of problems. thanks I cant determine the second term. For the first, I think you meant x sqrt(18) which reduces … 
Calculus
Please look at my work below: Solve the initialvalue problem. y'' + 4y' + 6y = 0 , y(0) = 2 , y'(0) = 4 r^2+4r+6=0, r=(16 +/ Sqrt(4^24(1)(6)))/2(1) r=(16 +/ Sqrt(8)) r=8 +/ Sqrt(2)*i, alpha=8, Beta=Sqrt(2) y(0)=2, e^(8*0)*(c1*cos(0)+c2*sin(0))=c2=2 … 
calculus  derivatives
can you please find the first 5 derivatives for: f(x) = (0.5e^x)(0.5e^x) f'(x) = ? 
Calculus: Derivatives
I'm having trouble understanding what derivatives in calculus (instantaneous speed) is. Can someone please explain it to me, or provide some easy links to learn from? 
math
I studied derivatives before, but kind of forgot them all, is there a website that gives me an overview of derivatives. What is first and second derivatives, how to find it, all the derivative rules and so on... thank you 
calculus
Find the first and second derivatives of the function. h(x) = sqrt x^2 + 1 
Calculus
Find the first and second derivatives of the given functions. y=¡î(x©÷+1) y'=x(x©÷+1)^(1/2) y"=[1(x©÷+1)^(1/2)][(1/2)[(x©÷+1)^(3/2)](2x)(x)] y"=[(x©÷+1)^(1/2)][(x©÷)(x©÷+1)^(3/2)] Is the second derivative right? 
Calculus
find the derivatives of the given functions. g(t)=sqrt t(1+t)/t^2 the sqrt is just over t. 
Derivatives
I have gotten so many different responses from mine on this question Can someone PLEASE write out the steps for me for this. Thanks f'(x)= 2x/(x^2+1) Find the second derivative. I get 4x^3 + x^2 12x + 1 
calculus
find the first and second derivatives for 3x^44xy^2+7=2y