Question #a16fd Calculus Graphing with the First Derivative Mean Value Theorem for Continuous Functions 1 Answer Jim H May 4, 2016 Use #d/dx(b^x) = b^x lnb# and the chain rule. Explanation: #b^x = e^(xlnb)#, so #d/dx(b^x) = e^(xlnb) * d/dx(xlnb) = e^(xlnb) *lnb = b^x lnb# For #f(x) = 3^(2x-4)#, apply the previous formula and the chain rule: #f'(x) = 3^(2x-4) ln3 (d/dx(2x-4)) = 2*3^(2x-4) ln3# So the exact value of #f'(2)# is #f'(2) = 2ln3# Answer link Related questions What is the Mean Value Theorem for continuous functions? What is Rolle's Theorem for continuous functions? How do I find the numbers #c# that satisfy the Mean Value Theorem for #f(x)=3x^2+2x+5# on the... How do I find the numbers #c# that satisfy the Mean Value Theorem for #f(x)=x^3+x-1# on the... How do I find the numbers #c# that satisfy the Mean Value Theorem for #f(x)=e^(-2x)# on the... How do I find the numbers #c# that satisfy the Mean Value Theorem for #f(x)=x/(x+2)# on the... How do I use the Mean Value Theorem to so #4x^5+x^3+2x+1=0# has exactly one real root? How do I use the Mean Value Theorem to so #2x-1-sin(x)=0# has exactly one real root? How do I find the numbers #c# that satisfy Rolle's Theorem for #f(x)=sqrt(x)-x/3# on the... How do I find the numbers #c# that satisfy Rolle's Theorem for #f(x)=cos(2x)# on the interval... See all questions in Mean Value Theorem for Continuous Functions Impact of this question 1159 views around the world You can reuse this answer Creative Commons License