How do you differentiate #y= 10^ (tan (pi)(theta)#? Calculus Differentiating Exponential Functions Differentiating Exponential Functions with Other Bases 1 Answer Azimet Jan 18, 2017 #dy/(dθ) = 10^tan(πθ) (πln(tan(πθ))) /cos^2(πθ)# Explanation: Let #v = πθ# and #u = tanv#. Using the chain rule, #dy/(dθ) = dy/(du) (du)/(dv) (dv)/(dθ)# So now, #y = 10^u#, so: #dy/(dθ) = 10^u lnu * 1/cos^2(v) * π# #= 10^tan(πθ) (πln(tan(πθ))) /cos^2(πθ)# Answer link Related questions How do I find #f'(x)# for #f(x)=5^x# ? How do I find #f'(x)# for #f(x)=3^-x# ? How do I find #f'(x)# for #f(x)=x^2*10^(2x)# ? How do I find #f'(x)# for #f(x)=4^sqrt(x)# ? What is the derivative of #f(x)=b^x# ? What is the derivative of 10^x? How do you find the derivative of #x^(2x)#? How do you find the derivative of #f(x)=pi^cosx#? How do you find the derivative of #y=(sinx)^(x^3)#? How do you find the derivative of #y=ln(1+e^(2x))#? See all questions in Differentiating Exponential Functions with Other Bases Impact of this question 4593 views around the world You can reuse this answer Creative Commons License