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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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3 years ago
Read 2 more answers
PLEASE ANSWER ASAP!!!!!!
Romashka [77]

The range in the average rate of change in temperature of the substance is from a low temperature of 1 F to a high of -11 F.

<h3>What is a formula for Fahrenheit?</h3>

The conversion formula for a temperature that is expressed on the Celsius (°C) scale to its Fahrenheit (°F) ;

°F = (9/5 × °C) + 32.

Given function:

f(x)= -6 sin(7/3 x+ 1/6) -5

The function will be maximum at the 7/3 x +1/6= 3π/2

So, the maximum temperature will be

= -6 sin (3π/2) -5

= 6 -5

= 1 F

The function will be minimum at the 7/3 x +1/6= π/2

Therefore, the maximum temperature will be

= -6 sin (π/2) - 5

= -6 -5

= -11 F

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brainly.com/question/26172293

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5 0
2 years ago
Simplify the expression.
Doss [256]
Distribute 6 thru the parenthesis=

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3 years ago
Factorise the following expressions​.
Setler79 [48]

Answer:

Q.1 a²+10a+24

splitting the middle.

a²+6a+4a+24

=a(a+6)+4(a+6)

(a+6)(a+4)

Q.2 x²+9x+18

splitting the middle

x²+6x+3x+18

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3 years ago
Enter a recursive rule for the geometric sequence. 6, −18, 54, −162, ...
svlad2 [7]

Answer:

The required recursive formula is:

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Step-by-step explanation:

We are given a geometric sequence as:

6,-18,54,-162,.....

Clearly after looking at different terms of the sequence we could observe that the sequence is an geometric progression (G.P.) with common ratio= -3 denoted by r.

Let a_n represents the nth term of the sequence.

This means that:

a_1=6, a_2=-18, a_3=54, a_4=-162,......

As the common ratio is -3.

so,

a_1=6\\\\a_2=-18=(-3)\times a_1\\\\a_3=54=(-3)\times a_2\\\\.\\.\\.\\.\\.\\.\\.\\.\\.a_n=(-3)\times a_{n-1}

Hence, the required recursive formula for the geometric sequence is:

a_n=(-3)\times a_{n-1}

5 0
3 years ago
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