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Galina-37 [17]
3 years ago
12

Y=sech(tan‐¹x) find the derivative ​

Mathematics
1 answer:
Klio2033 [76]3 years ago
8 0

Recall that

d/dx sech(x) = - sech(x) tanh(x)

d/dx tan⁻¹(x) = 1/(1 + x²)

Then by the chain rule,

dy/dx = - sech(x) tanh(x) / (1 + x²)

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Anastasia uses the equation p = 0.7(rh + b) to estimate the amount of take-home pay, p, for h hours worked at a rate of r dollar
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Complete question :

Anastasia uses the equation p = 0.7(rh + b) to estimate the amount of take-home pay, p, for h hours worked at a rate of r dollars per hour and any bonus received, b. What is an equivalent equation solved for h? A. h = (h equals StartFraction p Over 0.7 EndFraction minus b divided by r.– b)÷ r b. h = h equals StartFraction p Over 0.7 EndFraction minus b divided by r.– b ÷ r c. h = h equals left-parenthesis StartFraction p Over 0.7 EndFraction right-parenthesis divided by r minus b.÷ r – b d. h = h equals StartFraction p minus b Over 0.7 EndFraction divided by r. ÷ r

Answer:

[(p/0.7) - b] / r

A. h = (h equals StartFraction p Over 0.7 EndFraction minus b divided by r.– b)÷ r b. h = h equals StartFraction p Over 0.7 EndFraction minus b divided by r.

Step-by-step explanation:

Given the equation :

p = 0.7(rh + b)

Make h the subject

Divide both sides by 0.7

p / 0.7 = 0.7(rh + b) / 0.7

p/ 0.7 = rh + b

Subtract b from both sides :

(p/0.7) - b = rh + b - b

(p/0.7) - b = rh

Divide both sides by r

[(p/0.7) - b] / r = rh/ r

[(p/0.7) - b] / r = h

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