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

Question

2289 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-05-12T13:43:49

$d/dx(f(g(x))=-12sin12x$

As $f(x)=cos4x$ and $g(x)=-3x$ , $f(g(x))=cos4(-3x)$

According to chain rule

$d/dxf(g(x))=(df)/(dg)xx(dg)/(dx)$

Hence, as $f(g(x))=cos4(-3x)$

$d/dx(f(g(x))=-4sin4(-3x) xx(-3)$

= $12sin(-12x)=-12sin12x$

Answer 2 · 2016-05-12T13:46:56

$-12sin(12x)$

$(df)/(dx)=(df)/(dg)(dg)/(dx)$
$=-4sin(4g(x))xx(-3)$
$=12sin(4(-3x))$
$-12sin(12x)$

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