I'm still really new to calculus, and was confused about the definition of a derivative.
It was my understanding that the derivative was the slope or gradient at a given point on a curve on a graph.
However, when you have a function like y = x^5 the curve is constantly growing steeper. So, the derivative of x^5 would be 5x^4.
Therefore, 5x^4 is equal to 625x? So, assuming the slope is 625x, where exactly is this slope on the graph because the slope is constantly changing as the curve grows steeper?
Im obviously getting something confused, if someone can help clear this up I'd really appreciate it.