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This is a classic example of a question that may be asked in an oxbridge interview. Getting to the correct answer is certainly not the concern, but the student should think logically of the processes invo...

To answer this we will use implicit differentiation with respect to x. So start by differentiating each term. On the left hand side 0 differentiates to 0. On the right hand side 5x² differentia...

Since f(x) is a product of the two functions e^x and sin(x^2), we can use the product rule which states that if f(x)=g(x)h(x), then f'(x)=g'(x)h(x)+g(x)h'(x). Let g(x)=e^x and h(x)=sin(x^2). Since the dif...

ln is the natural log. The thing to remember with differentiating natural log is the simple formula U'/U. The U is whatever is in the brackets. This means we differentiate X^2 and divide it by X^2. X^2 ...

Potential is the potential energy per unit at a certain location. For example in a electric field the electric potential energy depends on both the location of the charge in the field and the charge we ar...