Home » Additional Resources » Differentiation

1.       Find the derivative of:
\begin{aligned}
y \ = \ {\Big(3x \ – \ 1 \Big)}^{3} \ \cos \frac{3}{2}x \ \sin \frac{3}{2}x .
\end{aligned}

Check here for my solution

2.       Find the derivative of:
\begin{aligned}
y \ = \ 2 \ {\csc}^{3} \Big(4\pi {x}^{3} \ – \ \frac{\pi}{2} \Big).
\end{aligned}

Check here for my solution

3.       Find the derivative of:
\begin{aligned}
y \ = \ \sqrt[3]{ 2 \ – \ \cot (1 \ – \ \sqrt{x}) }.
\end{aligned}

Check here for my solution

4.       Find the derivative of:
\begin{aligned}
\hspace{2em} y \ = \ \frac{ \tan x – \cot x }{ \cot x + \tan x }.
\end{aligned}

Check here for my solution

5.       Find the derivative of:
\begin{aligned}
\hspace{2em} y \ = \ \frac{ \sin t + \cos t }{ \sin t – \cos t }.
\end{aligned}

Check here for my solution

6.       Find the derivative of:
\begin{aligned}
\hspace{2em} y \ = \ \ \frac{ \sin 2t + \sin 5t \ – \ \sin t }{ \cos 2t + \cos 5t + \cos t }.
\end{aligned}

Check here for my solution

7.       If $ f(x) = -5 \sec 3x \ $ then find the value of $ f'(\frac{4 \pi}{9})$.

Check here for my solution

8.       Find the equation of the tangent line and the equation of normal line to the curve $ y = \dfrac{-3}{\cot 2x} \ $ at point where $ x = \frac{\pi}{3}. $

Check here for my solution

9.       Given that $ y = x^2 + 8x + 13 $
    (i)     find $ \frac{dy}{dx} $ and the value of $x$ for which $\frac{dy}{dx} {\small = 0} $
    (ii)     showing your working clearly, decide whether the point corresponding to this $x$ value is a maximum or minimum by considering the gradient either side of it
    (iii)     show that the corresponding $y$ value is -3
    (iv)     sketch the curve.

Check here for my solution

10.       Find $\frac{dy}{dx}$ when $ y = x^3 \ – \ x \ $ and show that $ y = x^3 \ – \ x \ $ is an increasing function for $ x < -\frac{1}{\sqrt{3}} \ $ and $ \ x > \frac{1}{\sqrt{3}}.$

Check here for my solution

Leave a Comment

Your email address will not be published.