d/dx (a^u) a is a constant
To find the derivative of a function of the form a^u, where a is a constant and u is a function of x, we can use the chain rule
To find the derivative of a function of the form a^u, where a is a constant and u is a function of x, we can use the chain rule.
The chain rule states that if we have a composition of functions, we can find the derivative by taking the derivative of the outer function and multiplying it by the derivative of the inner function.
In this case, the outer function is a^u and the inner function is u(x). Let’s denote the derivative of u with respect to x as du/dx.
Using the chain rule, the derivative of a^u with respect to x is given by:
d/dx (a^u) = (a^u) * (du/dx) * ln(a)
Here, ln(a) represents the natural logarithm of the constant base ‘a’.
So, to find the derivative of a^u, we multiply the original function by the derivative of the exponent (du/dx) and also multiply it by ln(a).
It’s important to note that the derivative of u(x) with respect to x, du/dx, has to be known in order to evaluate the derivative of a^u accurately.
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