Derivative of (cos(5x))^x

Derivative of (cos(5x))^x. Simple step by step solution, to learn. Simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

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Derivative of (cos(5x))^x: 


((cos(5*x))^x)'

(cos(5*x))^x*((x)'*ln(cos(5*x))+(x*(cos(5*x))')/cos(5*x))

(cos(5*x))^x*((x)'*ln(cos(5*x))+(x*-sin(5*x)*(5*x)')/cos(5*x))

(cos(5*x))^x*((x)'*ln(cos(5*x))+(x*-sin(5*x)*((5)'*x+5*(x)'))/cos(5*x))

(cos(5*x))^x*((x)'*ln(cos(5*x))+(x*-sin(5*x)*(0*x+5*(x)'))/cos(5*x))

(cos(5*x))^x*((x)'*ln(cos(5*x))+(x*-sin(5*x)*(0*x+5*1))/cos(5*x))

(cos(5*x))^x*((x)'*ln(cos(5*x))+(x*5*(-sin(5*x)))/cos(5*x))

(cos(5*x))^x*((x)'*ln(cos(5*x))+(x*-5*sin(5*x))/cos(5*x))

(cos(5*x))^x*(1*ln(cos(5*x))+(x*-5*sin(5*x))/cos(5*x))

(cos(5*x))^1

(-sin(5*x)*(5*x)')^x

(-sin(5*x)*((5)'*x+5*(x)'))^x

(-sin(5*x)*(0*x+5*(x)'))^x

(-sin(5*x)*(0*x+5*1))^x

(5*(-sin(5*x)))^x

(cos(5*x))^x*(ln(cos(5*x))+(-5*x*sin(5*x))/cos(5*x))

The calculation above is a derivative of the function f (x)

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