Question

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

Answer 1

Answer:

$\frac{df(x)}{dx}=20x$

Step-by-step 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

$\frac{df(x)}{dx}=20x$

hence the derivative of the function $f(x)=10x^{2}$ is $\frac{df(x)}{dx}=20x$

Answer 2

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

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

Step-by-step explanation:

See attachment.