How do you determine the derivative of this exponential function #f(x) = sqrt (3^x) / x^2#? Calculus Basic Differentiation Rules Quotient Rule 1 Answer Bill K. May 29, 2015 Write the function as #f(x)=\frac{3^{x/2}}{x^2}# and then use the Quotient Rule and the Chain Rule: #f'(x)=\frac{x^{2}\cdot ln(3)\cdot 3^{x/2}\cdot \frac{1}{2}-3^{x/2}\cdot 2x}{x^{4}}=\frac{3^{x/2}\cdot(ln(\sqrt{3})\cdot x-2)}{x^{3}}# Answer link Related questions What is the Quotient Rule for derivatives? How do I use the quotient rule to find the derivative? How do you prove the quotient rule? How do you use the quotient rule to differentiate #y=(2x^4-3x)/(4x-1)#? How do you use the quotient rule to differentiate #y=cos(x)/ln(x)#? How do you use the quotient rule to find the derivative of #y=tan(x)# ? How do you use the quotient rule to find the derivative of #y=x/(x^2+1)# ? How do you use the quotient rule to find the derivative of #y=(e^x+1)/(e^x-1)# ? How do you use the quotient rule to find the derivative of #y=(x-sqrt(x))/(x^(1/3))# ? How do you use the quotient rule to find the derivative of #y=x/(3+e^x)# ? See all questions in Quotient Rule Impact of this question 1595 views around the world You can reuse this answer Creative Commons License