d(ax)/dx
a
Assuming a is a constant and x is the variable with respect to which we are taking the derivative, we can use the power rule of differentiation to find the derivative of ax with respect to x.
The power rule states that if we have a function f(x) = x^n, then the derivative of f(x) with respect to x is given by:
f'(x) = nx^(n-1)
Applying the power rule here, we get:
d(ax)/dx = d(a(x^1))/dx [since a is a constant]
= a(d(x^1)/dx)
= a(1*x^(1-1))
= a*x^0
= a
Therefore, the derivative of ax with respect to x is simply a.
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