determine the derivative of f)(x) =(sin 3x)²
1. determine the derivative of f)(x) =(sin 3x)²
f(x)=(sin3x)^2
f'(x)=2(sin3x).cos3x.3
=3.(2sin3xcos3x) ----> 2sinacosa=sin2a
=3sin6x
2. what is the derivative of log7x
[tex] log(7x) [/tex]
We are dealing with composite function here. Hence, applying chain rule is the key.
Chain rule :
[tex] \frac{d}{dx} (g(f(x))) = {g}^{.} (f(x)) \times {f}^{.} (x)[/tex]
Thus :
[tex] \frac{d}{dx} ( log(7x) ) = \frac{1}{ ln(10)7x } \times 7 \\ = \frac{1}{ ln(10) x} [/tex]
3. Which of the following statements correctly describes the motion of the car shown by the velocity time graph
Mana dari pernyataan-pernyataan berikut benar menjelaskan gerakan mobil yang ditunjukkan oleh kecepatan waktu grafik.
4. Diagram 5 shows the graph of a quadratic function y = f(x)
a. y = 21+4x-x²
0 = 21+4x-x²
0 = (7-x)(3+x)
x = 7 atau x = -3
b. mencari sumbu simetri di turunan pertama:
y = 21+4x-x²
y' = 4 - 2x ; subtitusi y' = 0 (karena pada titik puncak, m=0)
0 = 4 - 2x
2x = 4
x = 2 ← sumbu simetri
5. The signature of the letter is shown by sentence
Jawaban:
The signature of the letter is shown by sentence
Tanda tangan surat itu ditunjukkan oleh
kalimat
Semoga Membantu
6. The expression of hope is shown by the sentence
Jawaban:
I hope i got 100 score in my test! Im so nervous!
Penjelasan:
smg membantu:) <3
7. What is y- intercept point of the graph below?
Jawaban:
(0,-6)
Penjelasan dengan langkah-langkah:
ingat bahwa y- intercept point (titik potong sumbu y) adalah titik yang memotong sumbu y (vertikal) dan titik bertemunya garis di x=0
lokasinya pada fungsi kuadrat adalah (0,c)
misal...
x² - 2x + 3
a = 1
b = -2
c=3
maka titik potong sumbu y adalah (0, 3)
--------
di grafik, titik potong sumbu y berada di (0,-6)
8. what is the area of the rectangle shown below?
Jawab:
Penjelasan dengan langkah-langkah:
The area= luas yaa
okee berarti sangat gampang kpk!
Luas persegi panjang= lebar x panjang
maka panjang= 5 3/4 =23/4 cm dan lebar=3 cm
L= pxl
= 23/4 x 3
=69/4
=17 1/4 cm atau 17,25 cm
9. What is the area of the right triangle shown below
ANSWER:
60.
Penjelasanya :
(theorema phytagoras) a=[tex]\sqrt{b^{2} -c^{2} }[/tex]
a= 17[tex]\sqrt{17^{2}-8^{2} } = \sqrt{289-64}[/tex]
a=[tex]\sqrt{225} =[/tex]15
(the area of the right triangle) :
1/2 x a x h
1/2 x 8 x 15
= 60
ur welcome:)
10. The derivative of y = 3x⁵ is y' =
Jawab:
[tex]y'=15x^4[/tex]
Penjelasan dengan langkah-langkah:
[tex]y=3x^5\\y'=5\times 3x^{5-1}\\y'=15x^4[/tex]
Semoga membantu!!!
11. The examples of derivative quantities
artinya contoh jumlah turunanArtinya: Para contoh menurun quantities
Semoga membantu:)
12. A mass of an ideal gas of volume v, at pressure p, undergoes a cycle of changes as shown in the graph.
Jawaban:
Sebuah massa gas ideal volume v, pada tekanan p, mengalami siklus perubahan seperti yang ditunjukkan pada grafik.
Penjelasan:
Translate:
A mass of an ideal gas of volume v, at pressure p, undergoes a cycle of changes as shown in the graph.
Sebuah massa gas ideal volume v, pada tekanan p, mengalami siklus perubahan seperti yang ditunjukkan pada grafik.
semoga membantu
13. i) the inverse of a function can exists if, and only if, the function f (x) is a one-one mappingii) the domain of f (x) is the domain if f^-1(x)iii) the graph f (x) & f^-1(x) are reflections of each other in the line y=xwhich statement is true?
Subject Function
Statement (i) is wrong. The correct one is that the inverse of the function exists if and only if the function mentioned is bijective function (one-to-one correspondence)
Statement (ii) is wrong. The domain of f(x) is the codomain of [tex] f^{-1}(x) [/tex]
Statement (iii) is wrong.
[tex] f(x) = x \Rightarrow f^{-1}(x)= x [/tex], while y = x and x = y is the same precise equation. The lines are conjoined and hence don't imply what the reflection means.
14. Data were collected on the fiber diameter and the fleece weight of wool taken from a sample of 20 sheep. the data are shown in the following graphs. graph 1 is a scatterplot of fleece weight versus fiber diameter with the respective least-squares regression line shown. graph 2 is the associated plot of the residuals versus the predicted values.
Penjelasan dengan langkah-langkah:
Pengambilan data diameter serat dan berat bulu domba diambil dari sampel sebanyak 20 ekor domba. data tersebut disajikan dalam grafik berikut. grafik 1 adalah sebaran berat bulu domba versus diameter serat dengan masing-masing garis regresi kuadrat terkecil ditampilkan. grafik 2 adalah plot terkait dari residu versus nilai yang diprediksi
15. The first derivative of the trigonometric function f(x) = tan x - 5 sinx is...~thank you for answering~ :):
Answer:
f'(X) = sec^x - 5 cosx
sedang tidak mood kakak??
16. What is the area of the triangle shown below
a = 5
b = 5
c = 8
Keliling
= a + b + c
= 5 + 5 + 8
= 18
s = 1/2 x keliling
s = 1/2 x 18
s = 9
Luas
= √(s(s - a)(s - b)(s - c))
= √(9(9 - 5)(9 - 5)(9 - 8))
= √(9 x 4 x 4 x 1)
= √144
= 12 satuan luas
17. if f'(x) is the first derivative of f(x) x^2(2x-1)^3, the value of f'(1) =... a.2 b.6 c.8 d.10 e.14pakai cara yaaa
u = x^2 v = (2x-1)^3
u' = 2x v' = 6(2x-1)^2
f'(1) = u' . v + u . v'
= 2x . (2x-1)^3 + x^2 . 6(2x-1)^2
= 2.1 (2.1-1)^3 + 1^2 . 6(2.1-1)^2
= 2 . 1 + 1 . 6
= 8 C
18. mohon bantuannya The picture is a graph of quadratic function......
Persamaan umum fungsi kuadrat :
f(x) = Ax² + Bx + C
Diketahui grafik fungsi f(x) melewati titik :
» (3 , 0)
=> f(3) = 0
=> A.(3)² + B.(3) + C = 0
=> 9A + 3B + C = 0 ( i )
» (–1 , 0)
=> f(–1) = 0
=> A.(–1)² + B.(–1) + C = 0
=> A - B + C = 0 ( ii )
» (0 , 3)
=> f(0) = 3
=> A.(0)² + B.(0) + C = 3
=> C = 3
Subtitusikan nilai C ke ( i ) :
9A + 3B + C = 0
9A + 3B + 3 = 0
9A + 3B = –3 ( iii )
Subtitusikan nilai C ke ( ii ) :
A - B + C = 0
A - B + 3 = 0
A - B = –3 ( iv )
Eliminasi ( iii ) dan ( iv ) :
( iii ) : 9A + 3B = –3
(iv) × 3 : 3A - 3B = –9
________________ +
12A = –12 => A = –1
Subtitusikan nilai A ke ( iv ) :
A - B = –3
–1 - B = –3 => B = 2
Substitusikan nilai A, B, dan C ke persamaan fungsi kuadrat :
f(x) = Ax² + Bx + C
f(x) = (–1)x² + (2)x + (3)
Jadi, persamaan fungsi kuadrat grafik tersebut adalah : f(x)=–x²+2x+3
19. a box weighing 300 newton is swung as shown in the figure. the amount of F required to pull the box is.....N
weight= force
if W is 300n. then F is 300N.
so the power to pull the box ia 300N
20. 3. Write down the expression of suggestion is shown is the text above
Jawaban:
Tuliskan ungkapan saran yang ditunjukkan adalah teks di atas
Penjelasan:
maksudnya diterjemahkan kan?
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