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3 years ago

How to find the answer

Mathematics

2 answers:

Valentin [98]3 years ago

6 0

-4+1= -3 -3•-6=18 first you add what's in the parentheses then multiply by the outside.

kari74 [83]3 years ago

5 0

I got C. -18 for my answer

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Find dy/dx for y= x^3 ln (cot x)

ICE Princess25 [194]

<h3>Answer</h3>

$\dfrac{dy}{dx} = 3x^2 \ln(\cot x)-x^3 \csc(x)\sec(x)$

<h3>Explanation</h3>

By the product rule $(d/dx)(f(x)g(x)) = f(x)g'(x) + g(x)f'(x)$ , we have

$\begin{aligned}\frac{dy}{dx} &= \left(x^3 \ln (\cot x) \right)' \\&= x^3\big(\ln (\cot x)\big)' + \ln (\cot x) \cdot \left(x^3\right)' \end{aligned}$

By the chain rule:

$\begin{aligned}\big(\ln (\cot x)\big)' &= \dfrac{1}{\cot x} \cdot (\cot x)' \\ &= \dfrac{1}{\cot x} \cdot -\csc^2 x\\&= -\tan (x) \csc^2(x) \\&= - \frac{\sin x}{\cos x} \cdot \frac{1}{\sin^2 x} = - \frac{1}{\cos x} \cdot \frac{1}{\sin x} \\&= -\csc(x)\sec(x)\end{aligned}$

By the power rule:

$(x^3)' = 3x^2$

thus

$\begin{aligned}\frac{dy}{dx} &= x^3\big(\ln (\cot x)\big)' + \ln (\cot x) \cdot \left(x^3\right)' \\&= x^3\big( -\csc(x)\sec(x) \big) + \ln(\cot x) \cdot (3x^2) \\&= -x^3 \csc(x)\sec(x) + 3x^2 \ln(\cot x) \\&= 3x^2 \ln(\cot x)-x^3 \csc(x)\sec(x)\end{aligned}$

Nothing to do to simplify any further, other than factoring out $x^2$ .

4 0

3 years ago

Help with practice problem

AlladinOne [14]

Answer

x^2 - y^2 x4

0.25 9

6 0

3 years ago

-3/v=-6 simply as much as possible

Aleksandr [31]

Hey!

In order to simplify this equation, we'll first have to multiply both sides of the equation by v. This will give us v on its own.

<em>Original Equation :</em>
$\frac{-3}{v} = -6$

<em>New Equation {Added Multiply Both Sides by V} :</em>
$\frac{-3}{v} v=-6v$

<em>Solution {New Equation Solved} :</em>
$-3 = -6v$

Now we'll switch sides to get v on the left side of the equation which is generally where we always want the variables to be located in these types of equations.

<em>Old Equation :</em>
$-3 = -6v$

<em>New Equation {Switched} :</em>
$-6v=-3$

Now we'll divide both sides by v to get v on its own.

<em>Old Equation :</em>
$-6v = -3$

<em>New Equation {Added Divide Both Sides by V} :</em>
$\frac{-6v}{v} = \frac{-3}{v}$

<em>Solution {New Equation Solved} :</em>
$v = \frac{1}{2}$

<em>So, this means that in the equation $\frac{-3}{v} =-6$ ,</em> $v = \frac{1}{2}$ .

Hope this helps!

- Lindsey Frazier ♥

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3 years ago

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AfilCa [17]

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Label and connect the coordinates above

aksik [14]

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3 years ago