(a^u)(ln a)(du/dx)
d/dx a^u
The given expression is:
(a^u)(ln a)(du/dx)
To solve this expression, we’ll need to use the chain rule of differentiation, which is given by:
d/dx[f(g(x))] = f'(g(x)) * g'(x)
Here, we can consider f(u) = a^u and g(x) = u(x), which gives us:
(a^u)(du/dx) = f'(g(x)) * g'(x)
To find f'(u), we can use the power rule of differentiation, which states that:
d/dx[a^u] = (ln a) * (a^u) * (du/dx)
Thus, if we substitute this in the above expression, we get:
(a^u)(ln a)(du/dx) = d/dx[a^u] * (du/dx) = (ln a) * (a^u) * (du/dx) * (du/dx)
Therefore, the final answer to the given expression is:
(a^u)(ln a)(du/dx) = (ln a) * (a^u) * (du/dx) * (du/dx)
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