How do you differentiate sqrt(4x² + 1)?

1 Answer
Jun 5, 2015

We'll use the power rule and the chain rule.

f(x)=sqrt(4x^2+1) = (4x^2+1)^(1/2)

So,

f'(x) = 1/2(4x^2+1)^(1/2-1)*d/dx(4x^2+1)

=1/2(4x^2+1)^(-1/2)*8x

=1/(2(4x^2+1)^(1/2)) * (8x)/1

= (4x)/sqrt(4x^2+1)

And the last line cannot be simplified any further, so we're finished.