Question

Using first principal find the gradient of the curve whose equation is y=x^5. show working pleas​

Answer 1

The gradient of
`y = x^(5)` is
`(dy)/(dx) = 5\cdot x^(4)`.

Explanation:

Geometrically speaking, the gradient of a curve is the slope of the tangent line at a given point of the curve. From perspective of Differential Calculus, the gradient is the first derivative of the curve. Let
`y = x^(5)`, then the gradient of the curve is:

`(dy)/(dx) = 5\cdot x^(4)` (1)

The gradient of
`y = x^(5)` is
`(dy)/(dx) = 5\cdot x^(4)`.