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3 years ago

Solve for x. x+1/3 - x+2/4 = x+3/6 A. x = -4 B. x = -11/3 C. x = -8

Mathematics

1 answer:

Alexeev081 [22]3 years ago

3 0

X+1/3 -+2/4 = x+3/6 = x= - 11/3

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Find the derivative for the function.

dalvyx [7]

The rule for deriving a multiplication is

$(f(x)\cdot g(x))' = f'(x)g(x)+f(x)g'(x)$

Also, we can forget about the factor 4 for now, since we have

$(4f(x)\cdot g(x))' = 4(f'(x)g(x)+f(x)g'(x))$

So, we will just multiply everything by 4 at the end. Our functions are

$f(x) = (x^7-9)^{12},\quad g(x) = (4x+8)^{11}$

For both derivatives we will use the rule

$(f(x)^n)' = n\cdot f(x)^{n-1}\cdot f'(x)$

So, we have

$f'(x) = 12\cdot(x^7-9)^{11}\cdot 7x^6,\quad g'(x) = 11\cdot(4x+8)^{10}\cdot 4$

We can simplify those expression a little bit:

$f'(x) = 84x^6(x^7-9)^{11},\quad g'(x) = 44(4x+8)^{10}$

The formula $f'(x)g(x)+f(x)g'(x)$ thus becomes

$84x^6(x^7-9)^{11}\cdot (4x+8)^{11} + (x^7-9)^{12} \cdot 44(4x+8)^{10}$

And so the final answer is

$4(84x^6(x^7-9)^{11}\cdot (4x+8)^{11} + (x^7-9)^{12} \cdot 44(4x+8)^{10})$

If you simplify this expression by factoring common terms, you will see that the correct answer is the first one.

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2 years ago

1. Consider f(x) = 3x - 5

Rzqust [24]

Answer:

Step-by-step explanation:

Here we have the function

$f(x)=3x-5$

We want to find the following ratio:

$\frac{f(x+h)-f(x)}{h}$

Note that the limit of this for $h\rightarrow 0$ is equivalent to the derivative of the function.

Here we have:

$f(x+h)=3(x+h)-5=3x+3h-5$

And

$f(x)=3x-5$

Therefore we have

$f(x+h)-f(x)=3x+3h-5-(3x-5)=3h$

And therefore,

$\frac{f(x+h)-f(x)}{h}=\frac{3h}{h}=3$

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3 years ago

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Answer:

T-6÷2+5

Step-by-step explanation:

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jolli1 [7]

Answer:40

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1 year ago

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Answer:

Step-by-step explanation:

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