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jok3333 [9.3K]
2 years ago
11

Find the derivative of sin2X​

Mathematics
2 answers:
murzikaleks [220]2 years ago
7 0

Answer:

2cos2x

Step-by-step explanation:

Using the Chain rule

\frac{d}{dx} (sin2x)

= cos2x × \frac{d}{dx} (2x)

= cos2x × 2

= 2cos2x

inn [45]2 years ago
5 0

Step-by-step explanation:

Derivation using Product rule : -

To find the derivative of f(x) = sin 2x by the product rule, we have to express sin 2x as the product of two functions. Using the double angle formula of sin, sin 2x = 2 sin x cos x. Let us assume that u = 2 sin x and v = cos x. Then u' = 2 cos x and v' = -sin x. By product rule,

f '(x) = uv' + vu'

= (2 sin x) (- sin x) + (cos x) (2 cos x)

= 2 (cos2x - sin2x)

= 2 cos 2x

This is because, by the double angle formula of cos, cos 2x = cos2x - sin2x.

Thus, derivation of sin 2x has been found by using the product rule.

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7 0
3 years ago
HH represents the height of the tree (in centimeters), t tt years since Renata moved in. H = 210 + 33 t H=210+33tH, equals, 210,
Jet001 [13]

Answer:

Therefore the rate of growth of the tree is 33 cm/ yr.

Step-by-step explanation:

Given that,

The height of the tree is

H= 210 +33t

Here H represent the height of tree in cm and t is time in year.

The rate of growth is the first order derivative of the H with respect to time.

i.e The rate of growth  =\frac{dH}{dt}

∴H= 210 +33t

Differentiating with respect to t

\frac{dH}{dt} =0 +33

\Rightarrow \frac{dH}{dt}=33

Therefore the rate of growth of the tree is 33 cm/ yr.

7 0
3 years ago
Factor completely <br><br> 81x^2-27x-18
Musya8 [376]
Find the greatest common factor which is 9 
9(9x^2-3x-2) and then factor the equation in the parenthesis 
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4 0
3 years ago
Find the value of -8 + 9 · 2 ÷ -3.
qaws [65]

Answer: -14

Step-by-step explanation:

You should get the right answer by following PEMDAS

6 0
3 years ago
Read 2 more answers
A researcher collects data on the relationship between the amount of daily exercise an individual gets and the percent body fat
fredd [130]

Answer: approximately 24

Step-by-step explanation:

We need to plot a regression line.

So we fit a model using the regression of Y on X, that an equation that predict Y for a given X using:

(Y -mean(Y ))= a(X-meanX)...........1

Where the formular of a is given the attachment.

N= the of individuals = 5

Y = amount of fat

X = time of exercise

mean(X )= sum of all X /N

= 131/5 = 26.2

mean(Y) = sum of all Y/N

= 104/5 = 20.8

a = N(SXY) - (SX)(SY)/ NS(X²) -(SX)²......2

SXY = Sum of Product X and Y

SX= sum of all X

SY = Sum of all Y

S(X²)= sum of all X²

(SX) = square of sum of X

a = -0.478

Hence we substitute into 1

Y-20.8 = -0.478 (X-26.2)

Y -20.8 = -0.478X - 12.524

Y = -0.478X + 33.324 or

Y = 33.324 - 0.478X (model)

When X = 20

Y = 33.324 - 0.478 × 20

Y = 33.324 - 9.56

Y = 23. 764

Y =24(approximately)

Carefully meaning of formula used in attachment to the solution they are the same.

4 0
3 years ago
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