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Nastasia [14]
3 years ago
9

Derivative of sin3x using first principle

Mathematics
1 answer:
Vera_Pavlovna [14]3 years ago
3 0

\displaystyle f(x)=\sin(3x)\\\\\\f'(x)=\lim_{h\to0}\dfrac{\sin(3(x+h))-\sin(3x)}{h}\\\\f'(x)=\lim_{h\to0}\dfrac{\sin(3x+3h)-\sin(3x)}{h}\\\\f'(x)=\lim_{h\to0}\dfrac{2\cos\left(\dfrac{3x+3h+3x}{2}\right)\sin\left(\dfrac{3x+3h-3x}{2}\right)}{h}\\\\f'(x)=\lim_{h\to0}\dfrac{2\cos\left(\dfrac{6x+3h}{2}\right)\sin\left(\dfrac{3h}{2}\right)}{h}\\\\f'(x)=\lim_{h\to0}\dfrac{2\cos\left(\dfrac{6x+3h}{2}\right)\sin\left(\dfrac{3h}{2}\right)}{\dfrac{3h}{2}}\cdot\dfrac{3}{2}

\displaystyle f'(x)=\lim_{h\to0}2\cos\left(\dfrac{6x+3h}{2}\right)\cdot\dfrac{3}{2}\\\\f'(x)=\lim_{h\to0}3\cos\left(\dfrac{6x+3h}{2}\right)\\\\f'(x)=3\cos\left(\dfrac{6x+3\cdot 0}{2}\right)\\\\f'(x)=3\cos\left(\dfrac{6x}{2}\right)\\\\f'(x)=3\cos(3x)

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Solve the following equation for y: 35x - 7y = 49, what is the slope?
agasfer [191]

Answer:

y = 5x - 7

slope = 5

Step-by-step explanation:

35x - 7y = 49

Subtract 35x from both sides.

-7y = -35x + 49

Divide both sides by -7.

y = 5x - 7

The equation is now in the slope-intercept form, y = mx + b, where m is the slope.

slope = m = 5

4 0
3 years ago
ms. lorenz needs to rent a car for 3 days. she can choose from two plans. plan a costs $60 per day. plan b costs $30 per day plu
maw [93]

Answer:

distance driven < 300 miles.

Step-by-step explanation:

Plan A

She needs the car for 3 days.

1 day costs 60 dollars

3 days cost 60*3 = 180 So this is the maximum amount that she can spend

Plan B

She still needs the car for 3 days

1 day costs 20 dollars of the car does not move

3 days costs 3*20 = 60 dollars.

60 + 0.4m < 180                Subtract 60

0.4m < 180 - 60

0.4m < 120                        Divide by 0.4

m < 120/ 0.4

m < 300  

Answer

so she should drive less than 300 miles.

3 0
3 years ago
Explain how you can use the graph of the quadratic function f(x) to solve the equation f(x)=0
Whitepunk [10]
F(x)=0
f(x)=y
so where y=0, the x value is the x in f(x)
basically, where the line crosses or touches the x axis, those ar the x values that make the function true
6 0
3 years ago
A bakery sold a total of 3028 coffee buns and blueberry buns. 1560 more coffee buns were sold than the blueberry buns. How many
Natali [406]

Answer:

\large{ \tt{ -  \: HEY  \: AH~\:♡ }}

\large{ \tt{✺ \: SOLUTION}} :

  • Provided : Total sold bakery items : 3028 coffee buns and blueberry buns & 1560 more coffee buns were sold than the blueberry buns.

  • To find : Number of coffee buns the bakery sold

- First , Subtract 1560 from 3028 :

\large{ \tt{→ \: 3028 - 1560 = 1468}}

We just subtacted the number of more coffee buns from the number of told items sold which means that the number of coffee buns and the number of blueberry buns sold are equal for now. Now divide 1428 by 2 :

\large{ \tt{→ \frac{1428}{2} = 734 }}

Now - Let's get back to the second sentence of the question and add 734 & 1560 :

\large{ \tt{→ \: 734 + 1560 =  \large{ \boxed{2294}}}}

  • Hence , The bakery sold 2294 coffee buns.

- Hope this helps , oneesan! ;)

7 0
3 years ago
HELP ASAP!! BEST ANSWER GETS BRAINLY! pls only answer if u know the answer this is a test!
Natali [406]

Answer:

It's the fourth one y=-1/6x+2/3

Step-by-step explanation:

4 0
3 years ago
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