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PREVIOUS ANSWERS

SCALCET9 3.3.005.

Differentiate.

h() = 02 sin()

n'(O) = 20 sin(0) + e-cos(0)

X

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SCALCET9 3.3.007.

Differentiate.

y = sec(0) tan()

(sin (0)2+1)

cos(0)3

OS

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SCALCET9 3.XP.3.009.

Find the derivative of the function.

F(t) = t cos(t) + 2 sin(t)

P”(t) = cos(x) + x sin(x) + x?cos(x)

>

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SCALCET9 3.3.015.MI.

Differentiate.

4x

y =

3-tan(x)

y’ = (12 cos(x)2 – 2 sin (2x) + 4x)/(3 cos (x) – sin (x)))

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SCALCET9 3.3.015.MI.SA.

5. [-13 Points]

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Tutorial Exercise

Differentiate.

y =

7x

4 – tan(x)

Step 1

We are given the function

y =

7x

4 – taní)

and need to find the derivative y’. If we let F(x) = 7x and g(x) = 4 – tan(x), we note that the given function is the quotient of the differentiable functions Fix) and g(x).

Fx)

900) )] Aviso Locos

16:9)

dx

g(x)f'(x) = f(x)g'(x)

ya

[of

To apply this rule, we first find the derivatives of Fx) = 7x and g(x) = 4-tan(x).

f(x) = 7%

F'(x) =

g(x) = 4 – tan(x)

g'(x) =

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SCALCET9 3.3.021.

Differentiate.

FO) = cos(e) sin()

F(@) =

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SCALCET9 3.3.023.

Show that

dx

(cs

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Tags:

functions

Derivatives

composite functions

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