How to Use the Chain Rule of Differentiation to Solve (a^u)(ln a)(du/dx)

(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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