Further Maths - Derivatives Cheat Sheet
Flashcards
2022-05-19
Standard Trig
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??
\[\csc(x)(\tan^2(x) + \csc^2(x))\]Hyperbolic Trig
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??
\[\csch(x)(\coth^2(x) + \csch^2(x))\]