The gradient of y=a^x
The value of a can be varied with the slider. Drag A to move the point along the curve.[br][br]Is there a value of a for which the gradient of the tangent is always the same as the y-value?
Differentiating y=ln(x)
Drag the point A along the curve y = e^x.[br][br]The gradient on y = ln x at A' is 1/(x-value at this point), therefore the gradient function for y = ln x is dy/dx = 1/x.