Further Maths - Derivatives Cheat Sheet

Pearson Edexcel Further Mathematics 2022


Flashcards

Standard trigonometric derivatives

What is the derivative of

\[\tan(x)\]

?

\[\sec^2(x)\]

What is the derivative of

\[\cot(x)\]

?

\[-\csc^2(x)\]

What is the derivative of

\[\sec(x)\]

?

\[\sec(x)\tan(x)\]

What is the derivative of

\[\csc(x)\]

?

\[-\csc(x)\cot(x)\]
\[\frac{\text{d}^2}{\text{d}x^2} \sec(x) = \frac{\text{d}}{\text{d}x} \sec(x)\tan(x) = ???\]

What is the second derivative here?

\[\sec(x)(\tan^2(x) + \sec^2(x))\]
\[\frac{\text{d}^2}{\text{d}x^2} \csc(x) = \frac{\text{d}}{\text{d}x} -\csc(x)\cot(x) = ???\]

What is the second derivative here?

\[\csc(x)(\cot^2(x) + \csc^2(x))\]

Hyperbolic trigonometric derivatives

What is the derivative of

\[\tanh(x)\]

?

\[\sech^2(x)\]

What is the derivative of

\[\sech(x)\]

?

\[-\sech(x)\tanh(x)\]

What is the derivative of

\[\csch(x)\]

?

\[-\csch(x)\coth(x)\]

What is the derivative of

\[\coth(x)\]

?

\[-\csch^2(x)\]
\[\frac{\text{d}^2}{\text{d}x^2} \sech(x) = \frac{\text{d}}{\text{d}x} -\sech(x)\tanh(x) = ???\]

What is the second derivative here?

\[\sech(x)(\tanh^2(x) - \sech^2(x))\]
\[\frac{\text{d}^2}{\text{d}x^2} \csch(x) = \frac{\text{d}}{\text{d}x} -\csch(x)\coth(x) = ???\]

What is the second derivative here?

\[\csch(x)(\coth^2(x) + \csch^2(x))\]