find the derivative of the function

Question

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

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

c) h(x)= (cos(2x)+1)^2

Answer 1

(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 : .

Step 2:

Derivative of constant : .

Solution :

The derivative of the function is .

Answer 2

(2)

Step 1:

The function is .

Apply derivative on each side with respect to x.

Use the quotient rule of derivatives : .

Use the sum and difference rule of derivatives : .

Use the derivative of constant : and

derivative of tangent function : .

Solution :

The derivative of the function is .

Answer 3

(3)

Step 1:

The function is .

Apply derivative on each side with respect to x.

Now use the power rule of derivatives : .

Use the sum and difference rule of derivatives : .

Use the derivative of constant : and

derivative of cosine function is .

Solution :

The derivative of the function is .