MAT 1300 Lecture Notes - Lecture 6: Product Rule

• School: University of Ottawa
• Department: Mathematics
• Course: MAT 1300
• Professor: Hung-Chang Liao

Document Summary

Continuation of lecture 5 f(x) = |x| what is f(0. 00001) ? answer =1. Let f be a function the line tangent to the graph of f at (a, f(a)) is the line passing through (a, f(a)) with slope f"(a) The derivative is a local property in the sense that if f and g agree near a point c then f" = g"(c ) Chain rule f and g are functions , then (fog)" (x) = f"(g(x)) . g"(x) if we write y= f(u) u= g(x) then df/dx = df/du . du/dx. Find the derivative of f(x) = (4x2 +5x)10. F is the composition of y= u10 and u=4x2 +5x. G is the composition of y= eu , u= x2+5. F"(x) = d/dx(e3x) . ln (5x+7 ) +e3x . d/dx(ln(5x+7): e3x is a composition of y= eu , u =3x d/dx (e3x) = eu . 3. =3e3x ln (5x+7) is the composition of y=ln(u) , u5x+7 d/dx (ln(5x+7))v= 1/u * 5.