Find the Derivative - d/dX y=8^(sin(piX))

Problem

d()/d(x)*8

Solution

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

2. Apply the chain rule by setting u=sin(π*x) which requires finding the derivative of the exponent.

3. Differentiate the exponent using the chain rule again for the inner function π*x where d(sin(π*x))/d(x)=cos(π*x)⋅π

4. Combine all parts into the final derivative formula.

5. Simplify the expression by rearranging the constant terms.

Final Answer

d(8)/d(x)=π*ln(8)*cos(π*x)*8

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