Answer
$\delta f(x)=9\cdot 10^x$
$\delta f(x)=(b-1)b^x$
Work Step by Step
We are given the function:
$f(x)=10^x$
Compute $\delta f(x)$:
$\delta f(x)=f(x+1)-f(x)=10^(x+1)-10^x=10^x\cdot 10-10^x$
$=10^x(10-1)$
$=9\cdot 10^x$
We got:
$\delta f(x)=9\cdot 10^x$
We are given the function:
$f(x)=b^x$
Compute $\delta f(x)$:
$\delta f(x)=f(x+1)-f(x)=b^(x+1)-b^x=b^x\cdot b-b^x$
$=b^x(b-1)$
$=(b-1)b^x$
We got:
$\delta f(x)=(b-1)b^x$
