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vredina [299]
3 years ago
6

Need help! Can anyone please help me? It would be much appreciated. Please view the attached photo. Will mark as brainliest!

Mathematics
1 answer:
Sergio [31]3 years ago
8 0

Answer:

  \text{D)} \quad y'=-10\csc{x}\cot{x}+\sec^2{x}

Step-by-step explanation:

  y=\dfrac{10}{\sin{x}}+\dfrac{1}{\cot{x}}=10\sin{(x)}^{-1}+\sin{(x)}\cos{(x)}^{-1}\\\\y'=-10\sin{(x)}^{-2}\cos{(x)}+\cos{(x)}\cos{(x)}^{-1}+\sin{(x)}^2\cos{{x}}^{-2}\\\\=-10\dfrac{1}{\sin{x}}\cdot\dfrac{\cos{x}}{\sin{x}}+1+\left(\dfrac{\sin{x}}{\cos{x}}\right)^2\\\\=-10\csc{x}\cot{x}+\sec^2{x}

_____

The product rule for derivatives applies.

  y = fg   ⇒   y' = f'g +fg'

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Enter a problem...

Calculus Examples

Popular Problems Calculus Find the Asymptotes f(x)=(2x^2)/(x^2-1)

f

(

x

)

=

2

x

2

x

2

−

1

Find where the expression

2

x

2

x

2

−

1

is undefined.

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1

,

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1

The vertical asymptotes occur at areas of infinite discontinuity.

x

=

−

1

,

1

Consider the rational function

R

(

x

)

=

a

x

n

b

x

m

where

n

is the degree of the numerator and

m

is the degree of the denominator.

1. If

n

<

m

, then the x-axis,

y

=

0

, is the horizontal asymptote.

2. If

n

=

m

, then the horizontal asymptote is the line

y

=

a

b

.

3. If

n

>

m

, then there is no horizontal asymptote (there is an oblique asymptote).

Find

n

and

m

.

n

=

2

m

=

2

Since

n

=

m

, the horizontal asymptote is the line

y

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a

b

where

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and

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1

.

y

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There is no oblique asymptote because the degree of the numerator is less than or equal to the degree of the denominator.

No Oblique Asymptotes

This is the set of all asymptotes.

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1

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