Find an equation of the line tangent

[gonzalo12345]

Homework Statement

f(x) = |sinx| for - π ≤ x ≤ π
g(x) = x^2
h(x)= g(f(x))

1. Find domain and range of h(x)
2. Find an equation of the line tangent to the graph of h at the point where x= π/4

Homework Equations

The Attempt at a Solution

It think that h(x) is (|sin x|)^2

so, is domain - π ≤ x ≤ π

here is where I am confused:

if d/dx (sin x) = cos x

then

is d/dx (|sin x|)^2 = (|cos x|)^2 ?

thanks in advance for the help.

 

[danago]

here is where I am confused:

if d/dx (sin x) = cos x

then

is d/dx (|sin x|)^2 = (|cos x|)^2 ?

thanks in advance for the help.

You can't do that. You should consider using the chain rule.

 

[gonzalo12345]

You can't do that. You should consider using the chain rule.

is there any rule for the derivate for an absolute value?

 

[Dick]

Squaring makes it easy to answer. |f(x)|^2=f(x)^2. Otherwise you have to split it into subdomains where f(x)>=0 and f(x)<0.

 

[HallsofIvy]

|x|= x if x\ge 0, -x is x< 0. Its derivative is 1 if x> 0, -1 if x< 0, not defined for x=0.