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grandymaker [24]
3 years ago
14

Find the derivative

Mathematics
1 answer:
zalisa [80]3 years ago
6 0

First use the chain rule; take y=\dfrac{x+5}{x^2+3}. Then

\dfrac{\mathrm df}{\mathrm dx}=\dfrac{\mathrm df}{\mathrm dy}\cdot\dfrac{\mathrm dy}{\mathrm dx}

By the power rule,

f(x)=y^2\implies\dfrac{\mathrm df}{\mathrm dy}=2y=\dfrac{2(x+5)}{x^2+3}

By the quotient rule,

y=\dfrac{x+5}{x^2+3}\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{(x^2+3)\frac{\mathrm d(x+5)}{\mathrm dx}-(x+5)\frac{\mathrm d(x^2+3)}{\mathrm dx}}{(x^2+3)^2}

\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{(x^2+3)-(x+5)(2x)}{(x^2+3)^2}

\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{3-10x-x^2}{(x^2+3)^2}

So

\dfrac{\mathrm df}{\mathrm dx}=\dfrac{2(x+5)}{x^2+3}\cdot\dfrac{3-10x-x^2}{(x^2+3)^2}

\implies\dfrac{\mathrm df}{\mathrm dx}=\dfrac{2(x+5)(3-10x-x^2)}{(x^2+3)^3}

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Salsk061 [2.6K]

Answer:

(3 V/ 4 pi) ^(1/3) =  r

Step-by-step explanation:

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V = 4/3 pi r^3

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3/4 V = 4/3*3/4 pi r^3

3/4 V = pi r^3

Divide each side by pi

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3 V/ 4 pi =  r^3

Take the cube root of each side

(3 V/ 4 pi) ^(1/3) = ( r^3) ^1/3

(3 V/ 4 pi) ^(1/3) =  r

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3 years ago
I need some help with this
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The angle of elevation from the hiker to the park ranger is the same as the angle of depression from the ranger to the hiker, 29°.

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Multiplying the equation by x/tan(29°) gives
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3 years ago
Let v1=(1, 6) and v2=(5, -3)
astraxan [27]

Answer:

See Explanation;

Step-by-step explanation:

The given vectors are;

v_1=\:\: and v_2=\:\:

a) To add or subtract two vectors, we add or subtract their corresponding components

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v_1+v_2=\:\:

v_1+v_2=\:\:

v_1-v_2=\:\:-\:\:

v_1-v_2=\:\:

v_1-v_2=\:\:

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kifflom [539]

Answer:

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Step-by-step explanation:

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Answer:

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