help?-derivatives -trig-functions-exponential logs-

Question

Answer 1

(1)

Step 1:

The function is .

Apply derivative on each side with respect to x.

Difference rule of derivative : .

Chain rule of derivative : .

Derivative of exponential function : .

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Solution :

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Answer 2

(2)

Step 1:

The function is .

Rewrite the function.

Apply derivative on each side with respect to x.

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Solution :

.

Answer 3

(3)

Step 1:

The function is .

Apply derivative on each side with respect to t.

.

Solution :

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Answer 4

(4)

Step 1:

The function is .

Rewrite the function.

Apply derivative on each side with respect to x.

.

Solution :

.

Answer 5

(5)

Step 1:

The function is .

Apply derivative on each side with respect to x.

Quotent rule of derivative : .

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Solution :

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Answer 6

(6)

Step 1:

The function is .

Apply derivative on each side with respect to a.

Quotent rule of derivative : .

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Solution :

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