Differentiate the following function.
g(t) = 6 sec(t) + 7 cot(t)
g'(t) = ?
I tried using the sum rule and got
g'(t) = $\displaystyle sec(t)tan(t) + sec^2(t)$
is that right?
The derivative of $\displaystyle cot(t)$ is $\displaystyle -csc^2(t)$, this can be shown by using the quotient rule to differentiate $\displaystyle cot(t)=\frac{cos(t)}{sin(t)}$. Also, you have to keep the constants. The derivative should be:
$\displaystyle g'(t)=6sec(t)tan(t)-7csc^2(t)$