# Math Help - derivatives of trig functions

1. ## derivatives of trig functions

Differentiate the following function.
g(t) = 6 sec(t) + 7 cot(t)

g'(t) = ?

I tried using the sum rule and got
g'(t) = $sec(t)tan(t) + sec^2(t)$

is that right?

2. Originally Posted by break
Differentiate the following function.
g(t) = 6 sec(t) + 7 cot(t)

g'(t) = ?

I tried using the sum rule and got
g'(t) = $sec(t)tan(t) + sec^2(t)$

is that right?
The derivative of $cot(t)$ is $-csc^2(t)$, this can be shown by using the quotient rule to differentiate $cot(t)=\frac{cos(t)}{sin(t)}$. Also, you have to keep the constants. The derivative should be:

$g'(t)=6sec(t)tan(t)-7csc^2(t)$