1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Mrac [35]
3 years ago
10

Find dy/dx if y= (cos x) ^ x

Mathematics
1 answer:
Elan Coil [88]3 years ago
5 0
Y = (cos x)^x
log y = log (cos x)^x = x log (cos x)
1/y dy/dx = x * 1/cos x * -sin x + log (cos x) = -xsin x / cos x + log (cos x) = log (cos x) - xtan x
dy/dx = y(log (cos x) - xtan x) = (cos x)^x (log (cos x) - xtan x)


You might be interested in
Find the probability. One digit from the number 3,151,221 is written on each of seven cards. What is the probability of drawing
Verizon [17]

Answer:

5/7

Step-by-step explanation:

7 0
3 years ago
Find the endpoint of the line segment
blondinia [14]

Answer:

(29,-13)

Step-by-step explanation:

You can tackle this for x and y coordinate separately.

For x, the line starts at -9 and is halfway at 10. The distance between -9 and 10 is 19 so it has another 19 to go, which puts the endpoint at 10+19=29.

Same for y: from 7 to -3 is 10 down, another 10 to go, puts you at -13.

Formula: x,y of midpoint is ((x1+x2)/2, (y1+y2)/2)

3 0
4 years ago
For the following integral, find the approximate value of the integral with 4 subdivisions using midpoint, trapezoid, and Simpso
PIT_PIT [208]

Answer:

\textsf{Midpoint rule}: \quad \dfrac{2\pi}{\sqrt[3]{2}}

\textsf{Trapezium rule}: \quad \pi

\textsf{Simpson's rule}: \quad \dfrac{4 \pi}{3}

Step-by-step explanation:

<u>Midpoint rule</u>

\displaystyle \int_{a}^{b} f(x) \:\:\text{d}x \approx h\left[f(x_{\frac{1}{2}})+f(x_{\frac{3}{2}})+...+f(x_{n-\frac{3}{2}})+f(x_{n-\frac{1}{2}})\right]\\\\ \quad \textsf{where }h=\dfrac{b-a}{n}

<u>Trapezium rule</u>

\displaystyle \int_{a}^{b} y\: \:\text{d}x \approx \dfrac{1}{2}h\left[(y_0+y_n)+2(y_1+y_2+...+y_{n-1})\right] \quad \textsf{where }h=\dfrac{b-a}{n}

<u>Simpson's rule</u>

\displaystyle \int_{a}^{b} y \:\:\text{d}x \approx \dfrac{1}{3}h\left(y_0+4y_1+2y_2+4y_3+2y_4+...+2y_{n-2}+4y_{n-1}+y_n\right)\\\\ \quad \textsf{where }h=\dfrac{b-a}{n}

<u>Given definite integral</u>:

\displaystyle \int^{2 \pi}_0 \sqrt[3]{\sin^2 (x)}\:\:\text{d}x

Therefore:

  • a = 0
  • b = 2π

Calculate the subdivisions:

\implies h=\dfrac{2 \pi - 0}{4}=\dfrac{1}{2}\pi

<u>Midpoint rule</u>

Sub-intervals are:

\left[0, \dfrac{1}{2}\pi \right], \left[\dfrac{1}{2}\pi, \pi \right], \left[\pi , \dfrac{3}{2}\pi \right], \left[\dfrac{3}{2}\pi, 2 \pi \right]

The midpoints of these sub-intervals are:

\dfrac{1}{4} \pi, \dfrac{3}{4} \pi, \dfrac{5}{4} \pi, \dfrac{7}{4} \pi

Therefore:

\begin{aligned}\displaystyle \int^{2 \pi}_0 \sqrt[3]{\sin^2 (x)}\:\:\text{d}x & \approx \dfrac{1}{2}\pi \left[f \left(\dfrac{1}{4} \pi \right)+f \left(\dfrac{3}{4} \pi \right)+f \left(\dfrac{5}{4} \pi \right)+f \left(\dfrac{7}{4} \pi \right)\right]\\\\& = \dfrac{1}{2}\pi \left[\sqrt[3]{\dfrac{1}{2}} +\sqrt[3]{\dfrac{1}{2}}+\sqrt[3]{\dfrac{1}{2}}+\sqrt[3]{\dfrac{1}{2}}\right]\\\\ & = \dfrac{2\pi}{\sqrt[3]{2}}\\\\& = 4.986967483...\end{aligned}

<u>Trapezium rule</u>

\begin{array}{| c | c | c | c | c | c |}\cline{1-6} &&&&&\\ x & 0 & \dfrac{1}{2}\pi & \pi & \dfrac{3}{2} \pi & 2 \pi \\ &&&&&\\\cline{1-6} &&&&& \\y & 0 & 1 & 0 & 1 & 0\\ &&&&&\\\cline{1-6}\end{array}

\begin{aligned}\displaystyle \int^{2 \pi}_0 \sqrt[3]{\sin^2 (x)}\:\:\text{d}x &  \approx \dfrac{1}{2} \cdot \dfrac{1}{2} \pi \left[(0+0)+2(1+0+1)\right]\\\\& = \dfrac{1}{4} \pi \left[4\right]\\\\& = \pi\end{aligned}

<u>Simpson's rule</u>

<u />

<u />\begin{aligned}\displaystyle \int^{2 \pi}_0 \sqrt[3]{\sin^2 (x)}\:\:\text{d}x & \approx \dfrac{1}{3}\cdot \dfrac{1}{2} \pi \left(0+4(1)+2(0)+4(1)+0\right)\\\\& = \dfrac{1}{3}\cdot \dfrac{1}{2} \pi \left(8\right)\\\\& = \dfrac{4}{3} \pi\end{aligned}

6 0
2 years ago
A coffee mug is 6 inches tall. Is a stack of 10 coffee mugs taller than 4 feet?
Alenkinab [10]
6 x 10 = 60 inches
feet  = 12 inches
60/12= 5 Feet (More than 4 Feet)

Answer = True
4 0
3 years ago
Read 2 more answers
Jake sold 39 tickets to the the school fair and Jeanie sold 12 tickets. What is the ratio in the simplest for of the number of t
amm1812
\frac{number\ of\ tickets\ Janne}{number\ of\ tickets\ Jake}=\frac{12}{39}=\frac{12:3}{39:3}=\frac{4}{13}\\\\Answer:\boxed{D.\ \frac{4}{13}}
7 0
3 years ago
Read 2 more answers
Other questions:
  • Jeff bought a new car $10,450. He know this car's value will decrease by 20% each year. Jeff writes the following function to mo
    15·1 answer
  • 20x100/2???????????????????????????????????????????????????????????????????????????????
    11·2 answers
  • A copy machine makes 143 copies in 3 minutes and 15 seconds. How many copies does it make per minute?
    13·2 answers
  • A 3 foot wide brick sidewalk is laid around a rectangular swimming pool. The outside edge of the sidewalk measures 30 feet by 40
    14·1 answer
  • PLEASE HELP ASAP?!!!!!!!
    12·1 answer
  • Linda opened a savings account with $450. She saves $225 per month. Joe opened his savings account the same month with $750. He
    10·1 answer
  • David has a thousand trees.
    6·2 answers
  • Which government agency works to maintain water and air quality in Florida?
    13·2 answers
  • Orlando's sports-card collection features players from four teams, as shown in the table below
    9·1 answer
  • Aunt Maggie’s car broke down on iterestate 10. Sams towing charges a $57 hoop up fee and $2.00 per mile towed. Reginas towing ch
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!