Question

Use your knowledge of the derivative to compute the limit given below:
\lim_{h \rightarrow 0} \frac{(x + h)^{3.75} - x^{3.75}}{h} .


The derivative that is being calculated is
\frac{dy}{dx} = .

Answer 1

\[\lim_{h \rightarrow 0} \frac{(x + h)^{3.75} - x^{3.75}}{h} \]
This is the derivative of \[x^{(3.75)}\]
We know that
\[\frac{d}{dx} x^n= nx^{n-1}\]
so
\[\huge \frac{d}{dx} x^{3.75}= 3.75x^{3.75-1}=3.75^x{2.75}\]

Answer 2

Sorry the last term is
\[\huge 3.75 x^{2.75}\]

Answer 3

thanks