What is the derivative of #m(x)= (5^x)(x^7)#? Calculus Basic Differentiation Rules Product Rule 1 Answer A. S. Adikesavan May 1, 2016 #m'(x)=5^x x^6(7+x ln 5)# Explanation: Using the rule for the product, #m'(x)=(5^x)(x^7)'+(x^7)(5^x)'#. #=7 x^6 5^x + x^7(e^(x ln 5))'# #=7 x^6 5^x + x^7(e^(x ln 5)) ln 5#, using function of function rule. #=7 x^6 5^x + x^7(5^x) ln 5#. #=5^x x^6(7+x ln 5)# 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 1353 views around the world You can reuse this answer Creative Commons License