To differentiate the function, d/dx a^x, we can use logarithmic differentiation.
Let y = a^x.
Taking the natural logarithm of both sides:
ln y = ln(a^x)
ln y = x * ln a
Now, differentiate both sides with respect to x:
1/y * (dy/dx) = ln a
Therefore,
dy/dx = y * ln a
Substituting back in y = a^x:
dy/dx = a^x * ln a
Therefore, the derivative of d/dx a^x is a^x * ln a.
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