-5+(-3).I know the answer is -8 but how because a negative plus a negative is a positive.

Mathematics

1 answer:

ira [324]2 years ago

8 0

Answer:

“two negatives = positive” rule works for multiplication and division.

Step-by-step explanation:

-5 + (-3) example

imagine a number line with 0 in the center. From (0) You move left 5 places to (-5) on the number line. Now you move another 3 more to the left (-3) and land on (-8).

You are combining the negatives. I hope this helps.

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If f is a differentiable function, find an expression for the derivative of each of the following functions

almond37 [142]

12a. Answer: d) x⁶ f'(x) + 6x⁵ f(x)

Step-by-step explanation:

Use the multiplication formula for derivatives:

y = a · b → y' = a'b + ab'

y = x⁶ · f(x)

a = x⁶ b = f(x)

a' = 6x⁵ b' = f'(x)

y' = a'b + ab'

y' = 6x⁵ f(x) + x⁶ f'(x)

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

Step-by-step explanation:

Use the division formula for derivatives:

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

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