All categories

2 years ago

Find the derivative of x³/tanx

Mathematics

1 answer:

juin [17]2 years ago

7 0

Answer:

Below.

Step-by-step explanation:

We apply the quotient rule:

dy/dx = ( tanx * 3x^2 - x^3 * sec^2x) / (tan^2 x)

= x^2( 3tanx - xsec^2x) / tan^2x

You might be interested in

A cooler contains fifteen bottles of sports drink: eight lemon-lime flavored and seven orange flavored

dem82 [27]

Answer:

Mutually exclusive,

$P(\text{Lemon-lime or orange})=\frac{2}{3}$

Step-by-step explanation:

Please consider the complete question:

Determine if the scenario involves mutually exclusive or overlapping events. Then find the probability.

A cooler contains twelve bottles of sports drink: four lemon-lime flavored, four orange flavored, and four fruit-punch flavored. You randomly grab a bottle. It is a lemon-lime or an orange.

Let us find probability of finding one lemon lime drink.

$P(\text{Lemon-lime})=\frac{\text{Number of lemon lime drinks}}{\text{Total drinks}}$

$P(\text{Lemon-lime})=\frac{4}{12}$

$P(\text{Lemon-lime})=\frac{1}{3}$

Let us find probability of finding one orange drink.

$P(\text{Orange})=\frac{\text{Number of orange drinks}}{\text{Total drinks}}$

$P(\text{Orange})=\frac{4}{12}$

$P(\text{Orange})=\frac{1}{3}$

Since probability of choosing a lemon lime doesn't effect probability of choosing orange drink, therefore, both events are mutually exclusive.

We know that probability of two mutually exclusive events is equal to the sum of both probabilities.

$P(\text{Lemon-lime or orange})=P(\text{Lemon-lime})+P(\text{Orange})$

$P(\text{Lemon-lime or orange})=\frac{1}{3}+\frac{1}{3}$

$P(\text{Lemon-lime or orange})=\frac{1+1}{3}$

$P(\text{Lemon-lime or orange})=\frac{2}{3}$

Therefore, the probability of choosing a lemon lime or orange is $\frac{2}{3}$ .

8 0

2 years ago

Bernoulli differential equation... y'+xy=xy^2

snow_lady [41]

$y'+xy=xy^2\implies y^{-2}y'+xy^{-1}=x$

Let $z=y^{-1}$ , so that $z'=-y^{-2}y'$ . Then the ODE becomes linear in $z$ with

$-z'+xz=x\implies z'-xz=-x$

Find an integrating factor:

$\mu(x)=\exp\left(\displaystyle\int-x\,\mathrm dx\right)=e^{-x^2/2}$

Multiply both sides of the ODE by $\mu$ :

$e^{-x^2/2}z'-xe^{-x^2/2}z=-xe^{-x^2/2}$

The left side can be consolidated as a derivative:

$\left(e^{-x^2/2}z\right)'=-xe^{-x^2/2}$

Integrate both sides with respect to $x$ to get

$e^{-x^2/2}z=e^{x^2/2}+C$

where the right side can be computed with a simple substitution. Then

$z=1+Ce^{x^2/2}$

Back-substitute to solve for $y$ .

$y^{-1}=1+Ce^{x^2/2}\implies y=\dfrac1{1+Ce^{x^2/2}}$

3 0

2 years ago

select the answer that correctly orders the set of numbers frome greatest to least. 26%, 1/5, 0.3, 0.09

spin [16.1K]

Change the numbers into percents
0.3-----30%
26%---26%
1/5-----20%
0.09-----9%

5 0

3 years ago

Read 2 more answers

Divide. Write your answer in simplest form. ÷4/9 7/12

max2010maxim [7]

(4/9) divided by (7/12) = 4/9 * 12/7 = 48/63 = 16/21

7 0

3 years ago

Jenny watched 27 movies that she thought were very good. She watched 45 movies over the whole year. Of the movies she watched, w

Serjik [45]

if we take 45 as the 100%, what is 27 off of it in percentage?

$\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 45&100\\ 27&x \end{array}\implies \cfrac{45}{27}=\cfrac{100}{x}\implies \cfrac{5}{3}=\cfrac{100}{x} \\\\\\ 5x=300\implies c=\cfrac{300}{5}\implies c=60$

6 0

3 years ago

Find the derivative of x³/tanx​

Find the derivative of x³/tanx