Differentiation is used to find the gradients of curves at specific points on the curve.
The differentiated form of a function is known as its bfirst derivative/b. Differentiating again gives the bsecond derivative/b.
If the original function is (\bm{y}), then the first derivative is (\bm{\dfrac{dy}{dx}}) and the second derivative is (\bm{\dfrac{d2y}{dx2}}).
If the original function is (\bm{f(x)}), then the first derivative is (\bm{f'(x)}) and the second derivative is (\bm{f''(x)}).
The first derivative (f'(x)) is the gradient of the tangent to the graph of (y=f(x)) at a general point ((x,y)). The first derivative is also known as the bgradient function/b.
The first derivative (\Big(\dfrac{dy}{dx}\Big)) is the rate of change of (y) with respect to (x).
The second derivative (\Big(\dfrac{d2y}{dx2}\Big)) is the rate of change of the first derivative (\Big(\dfrac{dy}{dx}\Big)) with respect to (x).
[b]uDifferentiation[/u]/b
The first derivative (\dfrac{dy}{dx}) or (f'(x)) is the gradient of the tangent to the graph of (y=f(x)) at a general point ((x,y)).