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Ira Lisetskai [31]
3 years ago
14

4. A Geometric Proof (4 points total) Here is another interesting proof. The smaller white square is inside a larger square. Eac

h blue area is a right triangle. To find the area of the white square, you can find the area of the big square and subtract the areas of the right triangles. b a 1 b b Area of big square = (a + b) Area of 4 triangles = 4 4 tab b Area of white square = big square - 4 shaded triangles a. Use these areas to write an equation for the area of the white square. Simplify the equation if possible. (2 points)​

Mathematics
1 answer:
Nady [450]3 years ago
5 0

Answer:im sorry its just for points

Step-by-step explanation:

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<u>Step-by-step explanation:</u>

Use the multiplication formula for derivatives:

y = a · b       →     y' = a'b + ab'

<u>y = x⁶ · f(x)     </u>  

a = x⁶          b = f(x)

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<u>y' = a'b + ab'</u>

y' = 6x⁵ f(x) + x⁶ f'(x)

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12b. Answer:  \bold{b)\ y=\dfrac{xf'(x)-9f(x)}{x^{10}}'}

<u>Step-by-step explanation:</u>

Use the division formula for derivatives:

y=\dfrac{a}{b}       →     y' = \dfrac{a'b - ab'}{b^2}

y=\dfrac{f(x)}{x^9}\\\\a=f(x)\qquad b=x^9\\\\a'=f(x)\qquad b'=9x^8\\\\y'=\dfrac{a'b-ab'}{b^2}\\\\y'=\dfrac{x^9f'(x)-9x^8f(x)}{(x^9)^2}\\\\.\ =\dfrac{x^9f'(x)-9x^8f(x)}{x^{18}}\\\\\text{factor out }x^{8}: y'=\dfrac{xf'(x)-9f(x)}{x^{10}}

Note: You can also move the denominator to the top (it will have a negative exponent) and use the multiplication formula for derivatives.

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