The derivative of with respect to is .

Differentiate using the Product Rule which states that is where and .

The derivative of with respect to is .

Multiply by by adding the exponents.

Multiply by .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

The derivative of with respect to is .

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Reorder terms.

By the Sum Rule, the derivative of with respect to is .

Evaluate .

Differentiate using the Product Rule which states that is where and .

The derivative of with respect to is .

Differentiate using the chain rule, which states that is where and .

To apply the Chain Rule, set as .

Differentiate using the Power Rule which states that is where .

Replace all occurrences of with .

The derivative of with respect to is .

Multiply by by adding the exponents.

Move .

Multiply by .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Evaluate .

Differentiate using the chain rule, which states that is where and .

To apply the Chain Rule, set as .

Differentiate using the Power Rule which states that is where .

Replace all occurrences of with .

The derivative of with respect to is .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Combine terms.

Reorder the factors of .

Add and .

By the Sum Rule, the derivative of with respect to is .

Evaluate .

Differentiate using the Product Rule which states that is where and .

The derivative of with respect to is .

Differentiate using the chain rule, which states that is where and .

To apply the Chain Rule, set as .

Differentiate using the Power Rule which states that is where .

Replace all occurrences of with .

The derivative of with respect to is .

Multiply by by adding the exponents.

Move .

Multiply by .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Evaluate .

Since is constant with respect to , the derivative of with respect to is .

Differentiate using the Product Rule which states that is where and .

The derivative of with respect to is .

Differentiate using the chain rule, which states that is where and .

To apply the Chain Rule, set as .

Differentiate using the Power Rule which states that is where .

Replace all occurrences of with .

The derivative of with respect to is .

Multiply by by adding the exponents.

Use the power rule to combine exponents.

Add and .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Simplify.

Apply the distributive property.

Combine terms.

Multiply by .

Remove unnecessary parentheses.

Reorder the factors of .

Add and .

Find the 2nd Derivative y=sec(x)