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Lucy (Student) March 19 2017
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This is a difficult question that you only need to know the result of.However, it's a good exercise to derive it.
Starting with f(x)=ax we can take the natural logarithm of both sides (so we can use one of its properties).
This gives us ln(f(x))=ln(ax), from the natural logarithms properties we know this is equal to ln(f(x))=x*ln(a).
Now using the chain rule we can differentiate both sides,
d(ln(f(x)))/dx= f'(x)/f(x), d(x*ln(a))/dx=ln(a)
so we now have f'(x)/f(x)=ln(a). Recalling that f(x)=ax this gives us the answer,
This is a typical further maths question, doing it correctly is a matter of carrying out a two-step process.
Start by finding the determinant of the matrix,
Then swap the entries a d and negate the other entries. After dividing by the determinant the inverse of A is given.
A^-1=1/(ad-bc)([d -b],[-c, a]).see more