Derivative of kx with Respect to x: Power Rule and Simplification.

d/dx [kx]

To find the derivative of the function f(x) = kx, where k is a constant, we can use the power rule of differentiation

To find the derivative of the function f(x) = kx, where k is a constant, we can use the power rule of differentiation. The power rule states that the derivative of x^n with respect to x is equal to n*x^(n-1). In this case, the derivative of kx with respect to x is:

d/dx [kx] = k * d/dx [x]

Applying the power rule, the derivative of x with respect to x is equal to 1:

d/dx [x] = 1

This gives us:

d/dx [kx] = k * 1

Simplifying further, we get:

d/dx [kx] = k

Therefore, the derivative of kx with respect to x is simply the constant k.

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