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Paraphin [41]
3 years ago
10

Differentiatey=tan (x^2-5x+6)​

Mathematics
1 answer:
slavikrds [6]3 years ago
5 0

Use the chain rule:

<em>y</em> = tan(<em>x</em> ² - 5<em>x</em> + 6)

<em>y'</em> = sec²(<em>x</em> ² - 5<em>x</em> + 6) × (<em>x</em> ² - 5<em>x</em> + 6)'

<em>y'</em> = (2<em>x</em> - 5) sec²(<em>x</em> ² - 5<em>x</em> + 6)

Perhaps more explicitly: let <em>u(x)</em> = <em>x</em> ² - 5<em>x</em> + 6, so that

<em>y(x)</em> = tan(<em>x</em> ² - 5<em>x</em> + 6)   →   <em>y(u(x))</em> = tan(<em>u(x)</em> )

By the chain rule,

<em>y'(x)</em> = <em>y'(u(x))</em> × <em>u'(x)</em>

and we have

<em>y(u)</em> = tan(<em>u</em>)   →   <em>y'(u)</em> = sec²(<em>u</em>)

<em>u(x)</em> = <em>x</em> ² - 5<em>x</em> + 6   →   <em>u'(x)</em> = 2<em>x</em> - 5

Then

<em>y'(x)</em> = (2<em>x</em> - 5) sec²(<em>u</em>)

or

<em>y'(x)</em> = (2<em>x</em> - 5) sec²(<em>x</em> ² - 5<em>x</em> + 6)

as we found earlier.

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3 years ago
Evaluate the expression when q=5 and b=9.<br> a+4b
Ierofanga [76]

Step-by-step explanation:

a = 5

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5 + 4×9 =

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lapo4ka [179]

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Step-by-step explanation:

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Answer:

Step-by-step explanation:

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3 years ago
Find the values of A, B, and C in the table.​
PilotLPTM [1.2K]

Answer:

A = 1

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B must be positive, so that, f(0) is above the x-axis, therefore, B = 2 is a correct choice.

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