If $f(x)= tan2 x$ and $g(x) = sqrt(-4x-3$ , how do you differentiate $f(g(x))$ using the chain rule?

Question

1886 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-11T02:48:20

$-(4sec^2(2sqrt(-4x-3))) /sqrt(-4x-3)$

Starting with: $f(x) = tan2x$ and $g(x)=sqrt(-4x-3) = (-4x-3)^(1/2)$

Let $h(x) = f(g(x)) = tan(2(sqrt(-4x-3)))$

$f'(x) = 2sec^2(2x)$
$g'(x) = (1/2)(-4)(-4x-3)^(-1/2) = -2/sqrt(-4x-3)$

Using the Chain Rule:

$h'(x) = f'(g(x))*g'(x)$

$h'(x) = 2sec^2(2sqrt(-4x-3))*-2/sqrt(-4x-3)$

$h'(x) = -(4sec^2(2sqrt(-4x-3)))/sqrt(-4x-3)$

If f(x)= tan2 x f(x)= tan2 x and g(x) = sqrt(-4x-3 g(x) = sqrt(-4x-3 , how do you differentiate f(g(x)) f(g(x)) using the chain rule?