【印刷可能】 y=e^-x 176020-Y e x logarithmic form
How Do You Find The Derivative Of Y E X X 1 2 Using The Quotient Rule Socratic Y = ex p e2x 4ex 2 2 The best way to check our work here might be to choose some simple values for x and evaluate both sides of the original equation using a calculator 4 ex e x ex e x = y We start by applying the hint, letting u = ex ex e x ex e x = y ex 1 ex ex 1 ex = y u 1 u u 1 u = y u 1 u u u1 u = y u2 1 u2 1 = y u2 1 Given #y=e^x# Differentiate using the chain rule, which states that, #dy/dx=dy/(du)*(du)/dx# Let #u=x,(du)/dx=1# Then, #y=e^u,dy/(du)=e^u# Combine the results together to get #dy/dx=e^u*1# #=e^u# Substitute back #u=x# to get the final answer #color(blue)(bar(ul=e^x)# Y e x logarithmic form
