Find the derivative of the following from first principle-x

Question

Toppr Admin · Accepted Answer

Let f-x-x2212-xThus using first principle-xA0-f-x2032-x-limh-x2192-0f-x-h-x2212-f-x-h-limh-x2192-0-x2212-x-h-x2212-x2212-x-h-limh-x2192-0-x2212-hh-x2212-1

Find the derivative of the following function from first principle:
$- x$

Let $f (x) = - x$
Thus using first principle
$f^{'} (x) = lim h \to 0 \frac{f (x + h) - f (x)}{h}$
$= lim h \to 0 \frac{- (x + h) - (- x)}{h}$
$= lim h \to 0 \frac{- h}{h} = - 1$

Find the derivative of the following function from first principle:−x

Let f(x)=−xThus using first principle f′(x)=limh→0f(x+h)−f(x)h=limh→0−(x+h)−(−x)h=limh→0−hh=−1

Find the derivative of the following function from first principle:
$- x$

Let $f (x) = - x$
Thus using first principle
$f^{'} (x) = lim h \to 0 \frac{f (x + h) - f (x)}{h}$
$= lim h \to 0 \frac{- (x + h) - (- x)}{h}$
$= lim h \to 0 \frac{- h}{h} = - 1$