14F - Differentiation of other functions
■ The content contained within this section is not required for VCE Mathematical Methods Units 1 and 2.
It is also possible to differentiate other functions including exponentials, logarithms, sine, cosine and tangent. For VCE Mathematical Methods Unit 1 and 2 this is not required; however, by the conclusion of Units 3 and 4 students should be able to understand and apply the following rules for differentiation:
\[\frac{d}{dx}(x^n)=nx^{n-1}\] |
\[\frac{d}{dx}(sin(ax))=a cos(ax)\] |
\[\frac{d}{dx}((ax+b)^n)=an(ax+b)^{n-1}\] |
\[\frac{d}{dx}(cos(ax))=-a sin(ax)\] |
\[\frac{d}{dx}(e^{ax})=ae^{ax}\] |
\[\frac{d}{dx}(tan(ax))=\frac{a}{cos^2(ax)}=a sec^2(ax)\] |
\[\frac{d}{dx}(log_e(x))=\frac{1}{x}\] |