The discussion focuses on finding the derivative dy/dx of the function y=(cosx)^x using the product rule and logarithmic differentiation. The initial attempt incorrectly applied the formula for the derivative of a^u, assuming a constant base. The correct approach involves rewriting the function as y=e^(x ln(cosx)) and applying the product rule, leading to the final answer of dy/dx=(cosx)^x*(ln(cosx)-xtanx). This method clarifies the differentiation process for functions where both the base and exponent are variable.
PREREQUISITESStudents studying calculus, particularly those focusing on differentiation techniques, as well as educators seeking to clarify the application of the product rule and logarithmic differentiation.
pugola12 said:Homework Statement
Find dy/dx of y=(cosx)^x
Homework Equations
d/dx of a^u=lna*a^u*u'
The Attempt at a Solution
I thougt I just had to follow the form shown above, and this is what I got.
y=(cosx)^x
dy/dx=ln(cosx)*(cosx)^x*1
dy/dx=ln(cosx)*(cosx)^x
However, the actual answer is (cosx)^x*(ln(cosx)-xtanx)
I don't understand where this comes from at all. Thanks for your input.