Question

Differentiate the following function.
h (θ) = 9 csc(θ) + 3 e^θ cot(θ)

Answer 1

h'(\theta) = -9csc(\theta)cot(\theta) + 3 [e^(\theta)cot(\theta) + e^(\theta)[-csc^2(\theta)]
= -9csc(\theta)cot(\theta) + 3e^(\theta)[cot(\theta) - csc^2(\theta)]

Answer 2

the derivative of e^x is x'e^x -> e^x, and for the trig functions, just memorize their derivatives.

Answer 3

csc'=-csccot
cot'=-csc^2

Answer 4

ty!!

Answer 5

\[\int\limits\limits\limits \left(3 e^{\theta } \text{Cot}[\theta ]-9 \text{Cot}[\theta ] \text{Csc}[\theta ]-3 e^{\theta } \text{Csc}[\theta ]^2\right) \, d\theta =\]
\[3 e^{\theta } \text{Cot}[\theta ]+9 \text{Csc}[\theta ] \]