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find the derivative of the function

0 votes
a) g(x) = sqrt(x^2 + 1) (2x-5)^3

b) f(x)=tanx/(tanx+1)

c) h(x)= (cos(2x)+1)^2
asked Feb 24, 2015 in CALCULUS by anonymous

3 Answers

0 votes

(1)

Step 1:

The function is .

Apply derivative on each side with respect to x.

Use the product rule of derivatives : .

Now use the power rule of derivatives : .

Use the sum and difference rule of derivatives : .

image

Step 2:

Derivative of constant : image.

image

Solution :

The derivative of the function is image.

answered Feb 24, 2015 by yamin_math Mentor
0 votes

(2)

Step 1:

The function is .

Apply derivative on each side with respect to x.

image

Use the quotient rule of derivatives : image.

image

Use the sum and difference rule of derivatives : .

image

Use the derivative of constant : and

derivative of tangent function : image.

image

Solution :

The derivative of the function is image.

answered Feb 24, 2015 by yamin_math Mentor
edited Feb 24, 2015 by yamin_math
0 votes

(3)

Step 1:

The function is image.

Apply derivative on each side with respect to x.

image

Now use the power rule of derivatives : .

image

Use the sum and difference rule of derivatives : .

image

Use the derivative of constant : image and

derivative of cosine function is image.

image

Solution :

The derivative of the function is image.

answered Feb 24, 2015 by yamin_math Mentor

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