Find the Derivative - d/dx 3^(cos(x))

Problem

d(3)/d(x)

Solution

1. Identify the rule for differentiating an exponential function with base a which is d(au)/d(x)=au*ln(a)d(u)/d(x)

2. Apply the chain rule by setting u=cos(x) which means we must multiply the derivative of the outer function by the derivative of the inner function.

3. Differentiate the inner function cos(x) to get −sin(x)

4. Combine the components to form the final derivative expression.

Final Answer

d(3)/d(x)=−3*ln(3)*sin(x)

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