fxex7x21 fxSolution ddxex7 x21 Use the quotient rule ddxuv

f(x)=e^x/7x^2+1

f\'(x)=

d/dx(e^x/(7 x^2+1)) | Use the quotient rule, d/dx(u/v) = (v ( du)/( dx)-u ( dv)/( dx))/v^2, where u = e^x and v = 7 x^2+1: = | ((7 x^2+1) (d/dx(e^x))-e^x (d/dx(7 x^2+1)))/(7 x^2+1)^2 | The derivative of e^x is e^x: = | ((7 x^2+1) e^x-e^x (d/dx(7 x^2+1)))/(7 x^2+1)^2 | Differentiate the sum term by term and factor out constants: = | (e^x (7 x^2+1)-e^x (7 (d/dx(x^2))+d/dx(1)))/(7 x^2+1)^2 | The derivative of 1 is zero: = | (e^x (7 x^2+1)-e^x (7 (d/dx(x^2))+0))/(7 x^2+1)^2 | The derivative of x^2 is 2 x: = | (e^x (7 x^2+1)-7 e^x (2 x))/(7 x^2+1)^2

$f(x)=e^x/7x^2+1 f\'(x)=Solution d/dx(e^x/(7 x^2+1)) | Use the quotient rule, d/dx(u/v) = (v ( du)/( dx)-u ( dv)/( dx))/v^2, where u = e^x and v = 7 x^2+1: = | ($

fxex7x21 fxSolution ddxex7 x21 Use the quotient rule ddxuv

Solution

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