How do you find the derivative of #f(z)=e^z(cosz)#? Calculus Basic Differentiation Rules Product Rule 1 Answer Timber Lin Apr 11, 2018 #f'(z)=e^z(cosz-sinz)# Explanation: use product rule: #f'(z)=d/dz(e^z)*cosz+d/dz(cosz)*e^z# #f'(z)=e^z*cosz-sinz*e^z# #f'(z)=e^z(cosz-sinz)# Answer link Related questions What is the Product Rule for derivatives? How do you apply the product rule repeatedly to find the derivative of #f(x) = (x - 3)(2 - 3x)(5 - x)# ? How do you use the product rule to find the derivative of #y=x^2*sin(x)# ? How do you use the product rule to differentiate #y=cos(x)*sin(x)# ? How do you apply the product rule repeatedly to find the derivative of #f(x) = (x^4 +x)*e^x*tan(x)# ? How do you use the product rule to find the derivative of #y=(x^3+2x)*e^x# ? How do you use the product rule to find the derivative of #y=sqrt(x)*cos(x)# ? How do you use the product rule to find the derivative of #y=(1/x^2-3/x^4)*(x+5x^3)# ? How do you use the product rule to find the derivative of #y=sqrt(x)*e^x# ? How do you use the product rule to find the derivative of #y=x*ln(x)# ? See all questions in Product Rule Impact of this question 3158 views around the world You can reuse this answer Creative Commons License