How do you find the derivative for #f(t)= te^(-t / 4)#? Calculus Basic Differentiation Rules Product Rule 1 Answer Binayaka C. Jun 23, 2018 #:f^' (t) = (4- t)/ (4 e ^(t/4)) # Explanation: # f (t) = t e ^(-t/4)# , Product rule : #d/dx (fg) = f g^'+g f^'# #:. f^' (t) = t * e ^(-t/4)*(-1/4)+ 1.e ^(-t/4) # #:. f^' (t) = e ^(-t/4)(1- t/4) # #:. f^' (t) = (4- t)/ (4 e ^(t/4)) # [Ans] 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 4380 views around the world You can reuse this answer Creative Commons License