Question

Find the derivative:

Answer 1

\[11X+\log _{4}(5x-17)\]

Answer 2

is this right: 11+ 1/(5x-17) X 1/ln4

Answer 3

\[11 + \frac{1}{(5x - 17)\ln4} * 5\]

Answer 4

where did the x5 come from?

Answer 5

\[\log_{4}(5x - 17) \] is a composite function so you have to use the chain rule to find the derivative of it

Answer 6

\[\frac{d}{dx}(\log_4(5x-17))=\frac{d}{dx}(\frac{\ln(5x-17)}{\ln(4)})=\frac{1}{\ln(4)}\cdot \frac{d}{dx}(\ln(5x-17))\]
\[=\frac{1}{\ln(4)} \cdot \frac{(5x-17)'}{5x-17}=\frac{1}{\ln(4)} \cdot \frac{5}{5x-17}\]

Answer 7

so first find the derivative of the outer function leaving the inner function alone \[\frac{1}{((5x-17)\ln4}\] Then multiply it by the derivative of the inner function which is 5