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Readme [11.4K]
3 years ago
5

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

Mathematics
2 answers:
Klio2033 [76]3 years ago
7 0

Answer:

dy/dx = [1/ln(10)][(2x+6)/(x^2 +6x)]

Step-by-step explanation:

See attachment

WARRIOR [948]3 years ago
3 0

Answer:

\dfrac{dy}{dx} =\dfrac{2 x + 6}{ \log{\left (10 \right )}\left(x^{2} + 6 x\right)}

Step-by-step explanation:

given

y = \log_{10}{(x^2+6x)}

using the property of log \log_ab=\frac{log_cb}{log_ca}, and if c =e,\log_ab=\frac{ln{b}}{ln{a}}, we can rewrite our function as:

y = \dfrac{\ln{\left (x^{2} + 6 x \right )}}{\ln{\left (10 \right )}}

now we can easily differentiate:

\dfrac{dy}{dx} = \dfrac{1}{\ln{10}}\left(\dfrac{d}{dx}(\ln{(x^{2} + 6x)})\right)

\dfrac{dy}{dx} = \dfrac{1}{\ln{10}}\left(\dfrac{2x+6}{x^{2} + 6x}\right)

\dfrac{dy}{dx} =\dfrac{2 x + 6}{ \log{\left (10 \right )}\left(x^{2} + 6 x\right)}

This is our answer!

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Answer:

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\implies\begin{cases}\dfrac{\mathrm dx_1}{\mathrm dt}=10-\dfrac1{10}x_1\\\\\dfrac{\mathrm dx_2}{\mathrm dt}=\dfrac1{10}x_1-\dfrac14x_2\\\\x_1(0)=10\\\\x_2(0)=15\end{cases}
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