Finding derivatives of trig functions.

Question

Find the derivative of the function.

y = 5tan(x^6) + sec(π/3)

 

So my teacher gave us this question to think about and I'm not sure how to approach it. Would you just use the product and chain rule like regular, and then take the inverse functions of the tan and sec? so for tan is could be cos/sin and then for sec it would be cos?... I am so confused. Please help me figure this out.

Thank you.

Answer 1

y = 5tan(x⁶) + sec(π/3)

 

sec(π/3) is a constant, so the derivative of sec(π/3) is zero.

 

So, dy/dx = 5sec²(x⁶)(x⁶)' + 0

 

              = 30x⁵sec²(x⁶)

Answer 2

You would use the Chain Rule on the first portion, that is, 5 tan(x⁶).

 

For the second portion, just take the derivative of the sec(pi/3)

 

The derivative of sec(pi/3) = 0

 

For the first half of the sum, the derivative is 5 sec²(x⁶) * (6x⁵) = 30x⁵ sec²(x⁶)

 

So y' = 30x⁵ sec²(x⁶)