Derivative of ln(e^(10x)cos(3x))

Derivative of ln(e^(10x)cos(3x)). 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 ln(e^(10x)cos(3x)): 


(ln(e^(10*x)*cos(3*x)))'

(1/(e^(10*x)*cos(3*x)))*(e^(10*x)*cos(3*x))'

(1/(e^(10*x)*cos(3*x)))*((e^(10*x))'*cos(3*x)+e^(10*x)*(cos(3*x))')

(1/(e^(10*x)*cos(3*x)))*(e^(10*x)*((10*x)'*ln(e)+(10*x*(e)')/e)*cos(3*x)+e^(10*x)*(cos(3*x))')

(1/(e^(10*x)*cos(3*x)))*(e^(10*x)*((10*x)'*ln(e)+(10*x*0)/e)*cos(3*x)+e^(10*x)*(cos(3*x))')

(1/(e^(10*x)*cos(3*x)))*(e^(10*x)*(((10)'*x+10*(x)')*ln(e)+(10*x*0)/e)*cos(3*x)+e^(10*x)*(cos(3*x))')

(1/(e^(10*x)*cos(3*x)))*(e^(10*x)*((0*x+10*(x)')*ln(e)+(10*x*0)/e)*cos(3*x)+e^(10*x)*(cos(3*x))')

(1/(e^(10*x)*cos(3*x)))*(e^(10*x)*((0*x+10*1)*ln(e)+(10*x*0)/e)*cos(3*x)+e^(10*x)*(cos(3*x))')

(1/(e^(10*x)*cos(3*x)))*(e^(10*x)*((10*x*0)/e+10*ln(e))*cos(3*x)+e^(10*x)*(cos(3*x))')

(1/(e^(10*x)*cos(3*x)))*(e^((10)'*x+10*(x)')*cos(3*x)+e^(10*x)*(cos(3*x))')

(1/(e^(10*x)*cos(3*x)))*(e^(0*x+10*(x)')*cos(3*x)+e^(10*x)*(cos(3*x))')

(1/(e^(10*x)*cos(3*x)))*(e^(0*x+10*1)*cos(3*x)+e^(10*x)*(cos(3*x))')

(1/(e^(10*x)*cos(3*x)))*(0^(10*x)*cos(3*x)+e^(10*x)*(cos(3*x))')

(1/(e^(10*x)*cos(3*x)))*(10*e^(10*x)*cos(3*x)+e^(10*x)*(cos(3*x))')

(1/(e^(10*x)*cos(3*x)))*(10*e^(10*x)*cos(3*x)+e^(10*x)*-sin(3*x)*(3*x)')

(1/(e^(10*x)*cos(3*x)))*(10*e^(10*x)*cos(3*x)+e^(10*x)*-sin(3*x)*((3)'*x+3*(x)'))

(1/(e^(10*x)*cos(3*x)))*(10*e^(10*x)*cos(3*x)+e^(10*x)*-sin(3*x)*(0*x+3*(x)'))

(1/(e^(10*x)*cos(3*x)))*(10*e^(10*x)*cos(3*x)+e^(10*x)*-sin(3*x)*(0*x+3*1))

(1/(e^(10*x)*cos(3*x)))*(10*e^(10*x)*cos(3*x)+e^(10*x)*3*(-sin(3*x)))

(1/(e^(10*x)*cos(3*x)))*(10*e^(10*x)*cos(3*x)+e^(10*x)*-3*sin(3*x))

(10*e^(10*x)*cos(3*x)-(3*e^(10*x)*sin(3*x)))/(e^(10*x)*cos(3*x))

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

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