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help derivatives-ex

0 votes

asked May 3, 2015 in CALCULUS by anonymous

7 Answers

0 votes

(1)

Step 1:

The function .

Apply derivative on each side with respect to x.

Apply power rule of derivatives : .

Therefore derivative of is .

Solution :

.

answered May 4, 2015 by yamin_math Mentor
0 votes

(2)

Step 1:

The function .

Apply derivative on each side with respect to x.

Apply product rule of derivatives : .

Derivative of cosine function is  .

Therefore derivative of is .

Solution :

.

answered May 4, 2015 by yamin_math Mentor
edited May 4, 2015 by yamin_math
0 votes

(3)

Step 1:

The function is .

Differentiate on each side with respect to x.

.

Quotient rule of derivatives .

image

Power rule of derivatives: and .

Therefore derivative of is .

Solution :

.

answered May 4, 2015 by yamin_math Mentor
edited May 4, 2015 by yamin_math
0 votes

(4)

Step 1:

The function .

Apply derivative on each side with respect to x.

Derivative of logarithm function : .

Power rule of derivatives: .

Therefore derivative of is .

Solution :

.

answered May 4, 2015 by yamin_math Mentor
edited May 4, 2015 by yamin_math
0 votes

(6)

Step 1:

The function .

Apply derivative on each side with respect to x.

Derivative of exponential function : .

Therefore derivative of is .

Solution :

.

answered May 4, 2015 by yamin_math Mentor
0 votes

(7)

Step 1:

The function .

Apply derivative on each side with respect to x.

Apply product rule of derivatives : .

Derivative of sine function is  .

Derivative of cot function is  .

Therefore derivative of is .

Solution :

.

answered May 4, 2015 by yamin_math Mentor
0 votes

(5)

Step 1:

The function .

Apply derivative on each side with respect to x.

Apply power rule of derivatives .

image

Therefore derivative of is image.

Solution :

image.

answered May 4, 2015 by yamin_math Mentor

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