Differentiate the following functions.

1.\( \displaystyle f(\theta)= \csc{\theta}\cot{\theta} \)


Solution


2. \( \displaystyle f(t)=\frac{3t^2+t}{1-\sec{t} }\)


Solution


3. \( \displaystyle f(u)= \sqrt[5]{u^3} \tan{u}\)


Solution


4. \( \displaystyle f(z)= \frac{a \sin{z}}{b+\cos{z}}\)


Solution


5. Find an equation of the tangent line to the curve \( \displaystyle f(x)= x\sin{x}\) at \((\pi,0)\).


Solution


6. If \(g(x)=x^2\cos{x}\) find \(g''(0)\).


Solution


7. Suppose that \(f(\pi/4)=-3\), \(f'(\pi/4)=4\), and \(h(x)=f(x)\tan{x} \). Find \(h'(\pi/4)\).


Solution