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kenny6666 [7]
2 years ago
6

Why is the rate of change of a slope secant and not tangent

Mathematics
1 answer:
BARSIC [14]2 years ago
4 0

Answer:

We cannot say that, as the slope could change based on the function we're considering.

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8 cm<br> 4 cm<br> 3cm. <br> 6cm <br><br> What is the area of the figure in square centimeters?
Dmitry [639]

Answer:

576 cm sqyared

Step-by-step explanation:

8 x 4 x 3 x 6 = 576

3 0
2 years ago
How to find the derivative of cos^2x? i seem to be confused.
slamgirl [31]
If you're using the app, try seeing this answer through your browser:  brainly.com/question/2927231

————————

You can actually use either the product rule or the chain rule for this one. Observe:

•  Method I:

y = cos² x

y = cos x · cos x


Differentiate it by applying the product rule:

\mathsf{\dfrac{dy}{dx}=\dfrac{d}{dx}(cos\,x\cdot cos\,x)}\\\\\\&#10;\mathsf{\dfrac{dy}{dx}=\dfrac{d}{dx}(cos\,x)\cdot cos\,x+cos\,x\cdot \dfrac{d}{dx}(cos\,x)}


The derivative of  cos x  is  – sin x. So you have

\mathsf{\dfrac{dy}{dx}=(-sin\,x)\cdot cos\,x+cos\,x\cdot (-sin\,x)}\\\\\\&#10;\mathsf{\dfrac{dy}{dx}=-sin\,x\cdot cos\,x-cos\,x\cdot sin\,x}


\therefore~~\boxed{\begin{array}{c}\mathsf{\dfrac{dy}{dx}=-2\,sin\,x\cdot cos\,x}\end{array}}\qquad\quad\checkmark

—————

•  Method II:

You can also treat  y  as a composite function:

\left\{\!&#10;\begin{array}{l}&#10;\mathsf{y=u^2}\\\\&#10;\mathsf{u=cos\,x}&#10;\end{array}&#10;\right.


and then, differentiate  y  by applying the chain rule:

\mathsf{\dfrac{dy}{dx}=\dfrac{dy}{du}\cdot \dfrac{du}{dx}}\\\\\\&#10;\mathsf{\dfrac{dy}{dx}=\dfrac{d}{du}(u^2)\cdot \dfrac{d}{dx}(cos\,x)}


For that first derivative with respect to  u, just use the power rule, then you have

\mathsf{\dfrac{dy}{dx}=2u^{2-1}\cdot \dfrac{d}{dx}(cos\,x)}\\\\\\&#10;\mathsf{\dfrac{dy}{dx}=2u\cdot (-sin\,x)\qquad\quad (but~~u=cos\,x)}\\\\\\&#10;\mathsf{\dfrac{dy}{dx}=2\,cos\,x\cdot (-sin\,x)}


and then you get the same answer:

\therefore~~\boxed{\begin{array}{c}\mathsf{\dfrac{dy}{dx}=-2\,sin\,x\cdot cos\,x}\end{array}}\qquad\quad\checkmark


I hope this helps. =)


Tags:  <em>derivative chain rule product rule composite function trigonometric trig squared cosine cos differential integral calculus</em>

3 0
3 years ago
What is 5 and 3 quarters
liraira [26]

Answer:

In general, 5 and 3 quarters would be 5.75 :)

Remember, there are 4 quarters in $1.00


7 0
3 years ago
Math: <br> -x + 6 is greater than or equal to 10
Alla [95]

Answer:

It is actually less than 10.

Step-by-step explanation:

7 0
3 years ago
Crickets can jump with a vertical velocity of up to 14 ft/s. Which equation models the height of such a jump, in feet, after t s
Natasha_Volkova [10]
Acceleration is simplified by assuming it is the constant -g

a=-g  we integrate this with respect to time to get v...

v=-gt+C  where C is the initial velocity in this case 14ft/s so

v=-gt+14  integrate again to get the height function

h=(-gt^2)/2 +14t +C  we are not given an initial height so C is 0

h(t)=14t-gt^2/2   letting g=32 and neatening up a bit...

h(t)=14t-16t^2
8 0
3 years ago
Read 2 more answers
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