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Here it is necessary to use the chain rule to solve the derivative. If we equate our equation in terms of the following notation: ln(x)='u'and 2x^2='v' and use the chain rule formula dy/dx=udv/dx+vdu/dx w...

sin2x = 2sinxcosx cos2x = cos^2(x) - sin^2(x) tan2x = (2tanx)/(1-tan^2(x))

1. substitute y=5x-2 into second equation --> x + 3(5x- 2)= 8// 2) factorise and simplify to get 16x=14 3) divide 14 by 16 to calculate the value of x to be 7/8 4) sub value of x into equation 1 to...

This question requires the use of two key rules of differentiating. The first of these is the product rule. The product rule describes a way of differentiating an equation which is the product of two diff...

The +c is to represent the loss in information after differentiation. Remember, integration is just the reverse of differentiation. Say we had this function:

f(x) = 2x^2 + 1 And we differentiate: f...