Differentiate the function (you cannot use the product or quotient rule here)

Question

1) h(x)=(sqrt(x)-(1/sqrt(x)))^2

2)g(x)=(e^2.5 + (1/(e^-x)))

Answer 1

Step 1:

(1)

The function is .

Simplify the function.

Apply derivative on each side with respect to x.

Use sum and difference rule of derivative : .

Use power rule of derivative : .

Use constant rule of derivative : .

Step 2:

(2)

The function is .

Apply derivative on each side with respect to x.

Use sum rule of derivative : .

Use constant rule of derivative : .

Use exponential function of derivative : .

Solution :

(1) .

(2) .