Differentiate : sin(t) / 2cos(t)

Question

Differentiate : sin(t) / 2cos(t)

 

 

ANSWER: F(t) = sec²(t) / 2

#17, practice exam

Answer 1

sin(t) / cos(t) = tan(t)  

 

The derivative of tan(t) is sec²(t), so the derivative of (1/2)tan(t) is (1/2)sec²(t)  

 

If you can't remember what the derivative of tan(t) is you can always use the quotient rule on  f(t) = sin(t) / 2cos(t)  

 

f'(t) = [ 2cos(t)*cos(t) - sin(t)*(-2sin(t)) ] / [ 4cos²(t) ]  

       = [ 2cos²(t) + 2sin²(t) ] / 4cos²(t)

       = 2[ cos²(t) + sin²(t) ] / 4cos²(t)

       = 2*(1) / 4cos²(t) 

       = 1 / 2cos²(t)

       = sec²(t) / 2

 

since sec(t) = 1 / cos(t)