Find $\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h }$ for $f ( x ) = \sqrt { x - 15 }$ .
A) $\sqrt { x - 15 }$
B) $\frac { 1 } { 2 \sqrt { x - 15 } }$
C) $\frac { \sqrt { x - 15 } } { 2 }$
D)limit does not exist
E) $\frac { 1 } { 15 \sqrt { x - 15 } }$

Question

Quizplus · Accepted Answer

This expression represents the definition of the derivative of $f(x) = \sqrt{x - 15}$ at a point $x$. Using the chain rule, the derivative of $f(x)$ with respect to $x$ is $\frac{1}{2\sqrt{x - 15}}$, which matches choice B.

Find lim⁡h→0f(x+h)−f(x)h\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h }limh→0​hf(x+h)−f(x)​

Find $\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h }$