Find an equation of the line tangent

  • #1

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.
 

Answers and Replies

  • #2
danago
Gold Member
1,122
4
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 cant do that. You should consider using the chain rule.
 
  • #3
You cant do that. You should consider using the chain rule.

is there any rule for the derivate for an absolute value?
 
  • #4
Dick
Science Advisor
Homework Helper
26,263
619
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.
 
  • #5
HallsofIvy
Science Advisor
Homework Helper
41,847
965
|x|= x if [itex]x\ge 0[/itex], -x is x< 0. Its derivative is 1 if x> 0, -1 if x< 0, not defined for x=0.
 

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