derivatives

Question

how do I find d/dx f(x) if f(x)=3x^2 ?

Answer 1

 

Hi Emma,

 

d/dx f(x) = lim_Δx→0 {f(x+Δx) - f(x)}/{(x+Δx) - x}

 

              = lim_Δx→0 {3(x+Δx)² - 3x²}/Δx

 

              = lim_Δx→0 {3x² + 6xΔx + 3(Δx)² - 3x²}/Δx

 

              = lim_Δx→0 {6xΔx + 3(Δx)²}/Δx

 

              = lim_Δx→0 (6x + 3Δx)

 

               = 6x