Question

Differentiate Functions of Other Bases In Exercise, find the derivative of the function.

f(x) = 10^x^2

Answer 1

Answer: for f(x) = 10^(x^2)

df(x)/dx = (2xln(10))10^(x^2)

Explanation:

See attachment.

Answer 2

`(df(x))/(dx)=20x\\`

Explanation:

to find the derivative of the function
`f(x)=10x^(2)` 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

`f(x)=10x^(2) \\`

increase x by Δx and and f(x) by Δf(x)

`f(x) +Δf(x)=10(x+Δx)^(2) \\`

if we expand we have

`f(x) +Δf(x)=10(x^(2)+2xΔx+(Δx)^(2))\\`

if we expand we have

`f(x) +Δf(x)=10x^(2)+20xΔx+10(Δx)^(2)\\`

next we subtract f(x) from both sides

`f(x) +Δf(x)-f(x)=10x^(2)+20xΔx+10(Δx)^(2)-f(x)\\`

`Δf(x)=10x^(2)+20xΔx+10(Δx)^(2)-10x^(2)\\`

`Δf(x)=20xΔx+10(Δx)^(2)\\`

Next we divide all through by Δx

`Δf(x)/Δx=20xΔx/Δx+10(Δx)^(2)/Δx\\`

`Δf(x)/Δx=20x+10Δx\\`

next we let the limit of Δx tends zero, we arrive at

`(df(x))/(dx)=20x\\`

hence the derivative of the function
`f(x)=10x^(2) \\` is
`(df(x))/(dx)=20x\\`