Write z=1-3i in exponential form

Mathematics

1 answer:

Sladkaya [172]3 years ago

7 0

Answer:

z=re ^iθ =2e ^i 3/π

Step-by-step explanation:

hope this helps

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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>

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3 years ago

The area of a rectangular bedroom is 240 square feet and the length is 16 feet what is the width

kirill [66]

1.) 240 divided by 16.
2.) 15
The width of the bedroom is 15 feet.

I hope this helps, please Brainliest me, and have a wonderful night! :D

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3 years ago

Read 2 more answers

Which of the equations is a line whose slope is 3/4 and y-intercept is 6? 3x - 4y = -6 3x - 4y = 6 3x - 4y = -24

Brut [27]

The answer is
3x-4y=-24

y=mx+b
-4y=-3x-24
y=(3/4)x+(-24/-4)
y=(3/4)x+6

slope m=3/4
y =6

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3 years ago

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Lady bird [3.3K]

Answer:

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3 years ago

Write 7*7*b*b*b in exponential form

ycow [4]

Answer:

7²b³

Step-by-step explanation:

An exponent signifies repeated multiplication. Here, the factor 7 is repeated twice, and the factor b is repeated 3 times. These will get exponents of 2 and 3, respectively:

7²b³

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3 years ago

Write z=1-3i in exponential form ​

Write z=1-3i in exponential form