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The derivative tells us how much the output of a function changes when we change the input by a tiny amount. For the function f(x) = x², we can think of the input as being a line of length x, a...

Let f(x)=y: y = e^(x²+4); To find the inverse of a function, you need to find x in terms of y. In this case, you need to bring the exponent to the base. So in order to bring x²+4 fro...

First, we note the centre of the circle is at the origin (0,0). Then we calculate the gradient of the line OP, the line connecting the origin to P. The gradient = change in y / change in x = (√7 - 0) / (3...

We know sin(x)^2+cos(x)^2=1Dividing by cos(x)^2: tan(x)^2+1=sec(x)^2Substitute into the Equation and Rearrange to get: tan(x)^2-2*tan(x)-3=0Let y = tan(x): y^2-2y-3=0Factorising: (y-3)(y+1)=0so y = 3 and ...

If y is inversely proportional to x. We know that y=k/x for some constant k. We need to find this constant before continuing. Looking at the information given to us in the question we know for one example...