Question

y= x to the power 3 find dy by dx​

Answer 1

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Answer 2

Explanation:

If y = some function of x (in other words if y is equal to an expression containing numbers and x's), then the derivative of y (with respect to x) is written dy/dx, pronounced "dee y by dee x" .

Differentiating x to the power of something

1) If y = xn, dy/dx = nxn-1

2) If y = kxn, dy/dx = nkxn-1(where k is a constant- in other words a number)

Therefore to differentiate x to the power of something you bring the power down to in front of the x, and then reduce the power by one.

Examples

If y = x4, dy/dx = 4x3

If y = 2x4, dy/dx = 8x3

If y = x5 + 2x-3, dy/dx = 5x4 - 6x-4