Answer:
[tex]\frac{df(x)}{dx}=20x\\[/tex]
Step-by-step explanation:
to find the derivative of the function [tex]f(x)=10x^{2}[/tex] we use the chain rule approach. which simply involves increasing x by Δx and carrying out simple arithmetic operation.
The First step is to increase x by Δx
[tex]f(x)=10x^{2} \\[/tex]
increase x by Δx and and f(x) by Δf(x)
[tex]f(x) +Δf(x)=10(x+Δx)^{2} \\[/tex]
if we expand we have
[tex]f(x) +Δf(x)=10(x^{2}+2xΔx+(Δx)^{2})\\[/tex]
if we expand we have
[tex]f(x) +Δf(x)=10x^{2}+20xΔx+10(Δx)^{2}\\[/tex]
next we subtract f(x) from both sides
[tex]f(x) +Δf(x)-f(x)=10x^{2}+20xΔx+10(Δx)^{2}-f(x)\\[/tex]
[tex]Δf(x)=10x^{2}+20xΔx+10(Δx)^{2}-10x^{2}\\[/tex]
[tex]Δf(x)=20xΔx+10(Δx)^{2}\\[/tex]
Next we divide all through by Δx
[tex]Δf(x)/Δx=20xΔx/Δx+10(Δx)^{2}/Δx\\[/tex]
[tex]Δf(x)/Δx=20x+10Δx\\[/tex]
next we let the limit of Δx tends zero, we arrive at
[tex]\frac{df(x)}{dx}=20x\\[/tex]
hence the derivative of the function [tex]f(x)=10x^{2} \\[/tex] is [tex]\frac{df(x)}{dx}=20x\\[/tex]
Answer: for f(x) = 10^(x^2)
df(x)/dx = (2xln(10))10^(x^2)
Step-by-step explanation:
See attachment.
