Activity 2.6.4

Determine the derivative of each of the following functions.

1. $\displaystyle f(x) = x^3 \arctan(x) + e^x \ln(x)$

2. $\displaystyle p(t) = 2^{t\arcsin(t)}$

3. $\displaystyle h(z) = (\arcsin(5z) + \arctan(4-z))^{27}$

4. $\displaystyle s(y) = \cot(\arctan(y))$

5. $\displaystyle m(v) = \ln(\sin^2(v)+1)$

6. $\displaystyle g(w) = \arctan\left( \frac{\ln(w)}{1+w^2} \right)$