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BARSIC [14]
3 years ago
11

Differentiating Functions of Other Bases In Exercise, find the derivative of the function.

Mathematics
1 answer:
aniked [119]3 years ago
7 0

Answer:

\dfrac{dy}{dx} = \frac{2x-3}{\ln 16(x^2 - 3x)}

Step-by-step explanation:

We are given the following in the question:

y = \ln {16}(x^2 - 3x)

We have to find the derivative of the given expression.

y = \ln 16(x^2 - 3x)\\\text{Using the log propert}\\\\\log_a b = \dfrac{\log b}{\log a}\\\\dfrac{d(x^n)}{dx} = nx^{n-1}\\\\\dfrac{d(\log x)}{dx} = \dfrac{1}{x}\\\\\text{\bold{Differentiating we get}}\\\\\displaystyle\frac{dy}{dx} = \frac{d(\ln 16(x^2-3x))}{dx}\\\\= \frac{1}{16(x^2-3x)})\frac{d(x^2-3x)}{dx}\\\\=\frac{1}{\log 16(x^2-3x)}(2x - 3)\\\\= \frac{2x-3}{\ln 16(x^2 - 3x)}

\dfrac{dy}{dx} = \frac{2x-3}{\ln 16(x^2 - 3x)}

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See attachment for grid

Required

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