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2 years ago

Help Which graph has x-intercepts of -3 and 4?

Mathematics

1 answer:

Tju [1.3M]2 years ago

4 0

Answer:

the last graph

Step-by-step explanation:

bcoz the curve touching -3 and 4 on x axis

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

3 0

3 years ago

4. A local restaurant employs 80 full time employees. Approximately 4/5 of the full-time employees are

laila [671]

Answer:

part-time work as a percentage of total part-time work, selected Latin American countries, 2003–13 .

396 pages

Step-by-step explanation:

nothin

3 0

2 years ago

Dimensions of a prism has a scale factor of 7/4 how will this affect surface area<br><br> Plz help

Margaret [11]

The surface area will increase by a factor of 49/16

6 0

3 years ago

T/F every function is a relation

sammy [17]

True
Every function is a relation, but not every relation is a function.

Hope this helps :)

4 0

2 years ago

Read 2 more answers

If there was an online shopping site was selling about 420 items per second. At this rate, how many items would it sell in 30 mi

Evgen [1.6K]

Answer:

756000

Step-by-step explanation:

You will multiply 30x60(There are 60 seconds in a min)=1800

Then Multiple 420x1800=756000

6 0

2 years ago