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 4 cm 3cm. 6cm 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:

$\mathsf{\dfrac{dy}{dx}=\dfrac{d}{dx}(cos\,x\cdot cos\,x)}\\\\\\
\mathsf{\dfrac{dy}{dx}=\dfrac{d}{dx}(cos\,x)\cdot cos\,x+cos\,x\cdot \dfrac{d}{dx}(cos\,x)}$

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

$\mathsf{\dfrac{dy}{dx}=(-sin\,x)\cdot cos\,x+cos\,x\cdot (-sin\,x)}\\\\\\
\mathsf{\dfrac{dy}{dx}=-sin\,x\cdot cos\,x-cos\,x\cdot sin\,x}$

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

—————

• Method II:

You can also treat y as a composite function:

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

and then, differentiate y by applying the chain rule:

$\mathsf{\dfrac{dy}{dx}=\dfrac{dy}{du}\cdot \dfrac{du}{dx}}\\\\\\
\mathsf{\dfrac{dy}{dx}=\dfrac{d}{du}(u^2)\cdot \dfrac{d}{dx}(cos\,x)}$

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

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

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: derivative chain rule product rule composite function trigonometric trig squared cosine cos differential integral calculus

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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

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3 years ago

Math: -x + 6 is greater than or equal to 10

Alla [95]

Answer:

It is actually less than 10.

Step-by-step explanation:

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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

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