Given,

y = x⁴ – 2x³ + 3x² + x + 5

We need to rate of change of f(x) w.r.t x.

Rate of change of a function w.r.t a given variable is obtained by differentiating the function w.r.t that variable only.

So in this case we will be finding dy/dx

As, y = x⁴ – 2x³ + 3x² + x + 5

Now, differentiating both sides w.r.t x –

∴ )

Using algebra of derivatives –

⇒

Use:

∴

⇒

∴ Rate of change of y w.r.t x is given by –