Mathematics, 15.07.2019 19:00 farihasy6508

Find the derivative of the trigonometric function

Answers: 1

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Answer from: ivilkas23

E. $\displaystyle f'(s) = s^5 \sec^2 s + 5s^4 \tan x$

General Formulas and Concepts:

Calculus

Differentiation

DerivativesDerivative Notation

Derivative Property [Addition/Subtraction]: $\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]$

Basic Power Rule:

f(x) = cxⁿf’(x) = c·nxⁿ⁻¹

Derivative Rule [Product Rule]: $\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)$

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle f(s) = s^5 \tan s$

Step 2: Differentiate

Derivative Rule [Product Rule]: $\displaystyle f'(s) = (s^5)' \tan s + s^5(\tan s)'$ Basic Power Rule/Trigonometric Differentiation: $\displaystyle f'(s) = 5s^4 \tan s + s^5 \sec^2 x$ Rewrite: $\displaystyle f'(s) = s^5 \sec^2 s + 5s^4 \tan x$

∴ Our answer is E.

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Answer from: Quest

sum= when you add is how much the whole amount is

distance= when you use angles and it means how far it goes

step-by-step explanation:

Answer from: Quest

answer:

payment just for service

→

87.12

payment for service including tax

→

94.09

explanation:

service only with 20% tip

→

72.6

(

100

)

87.12

in the opening of the question the word 'service' is associated only with the pretax value.

the closing part of the question asks: how much did she pay for the

service

−−−−−−

so technically the answer is

→

72.6

(

100

)

87.12

however, the intention of the question provider may have been that your answer is to be

87.12

(

100

)

94.09

to 2 decimal places.

payment just for service

→

87.12

payment for service including tax

→

94.09

tony b

mar 21, 2017

answer:

trying to explain it another way

explanation:

service charge

→

72.60

20% tip

100

72.60

14.52

−−−−−−

←

add

87.12

tax

100

87.12

6.97

−−−−−

←

add

94.09

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Find the derivative of the trigonometric function
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