Simplify the limit argument.

Multiply and .

Combine terms.

To write as a fraction with a common denominator, multiply by .

To write as a fraction with a common denominator, multiply by .

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Multiply and .

Multiply and .

Reorder the factors of .

Combine the numerators over the common denominator.

Simplify the limit argument.

Multiply the numerator by the reciprocal of the denominator.

Multiply and .

Move the term outside of the limit because it is constant with respect to .

Apply L’Hospital’s rule.

Evaluate the limit of the numerator and the limit of the denominator.

Take the limit of the numerator and the limit of the denominator.

Evaluate the limit of the numerator.

Take the limit of each term.

Split the limit using the Sum of Limits Rule on the limit as approaches .

Split the limit using the Sum of Limits Rule on the limit as approaches .

Evaluate the limits by plugging in for all occurrences of .

Evaluate the limit of which is constant as approaches .

Evaluate the limit of which is constant as approaches .

Evaluate the limit of by plugging in for .

Combine the opposite terms in .

Add and .

Subtract from .

Evaluate the limit of the denominator.

Take the limit of each term.

Split the limit using the Product of Limits Rule on the limit as approaches .

Split the limit using the Sum of Limits Rule on the limit as approaches .

Evaluate the limits by plugging in for all occurrences of .

Evaluate the limit of which is constant as approaches .

Evaluate the limit of by plugging in for .

Evaluate the limit of by plugging in for .

Simplify the answer.

Add and .

Multiply by .

The expression contains a division by The expression is undefined.

Undefined

The expression contains a division by The expression is undefined.

Undefined

The expression contains a division by The expression is undefined.

Undefined

Since is of indeterminate form, apply L’Hospital’s Rule. L’Hospital’s Rule states that the limit of a quotient of functions is equal to the limit of the quotient of their derivatives.

Find the derivative of the numerator and denominator.

Differentiate the numerator and denominator.

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

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

Evaluate .

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

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

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

Differentiate using the Power Rule which states that is where .

Add and .

Multiply by .

Subtract from .

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

Differentiate using the Power Rule which states that is where .

Multiply by .

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

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

Add and .

Differentiate using the Power Rule which states that is where .

Multiply by .

Add and .

Reorder terms.

Split the limit using the Limits Quotient Rule on the limit as approaches .

Split the limit using the Sum of Limits Rule on the limit as approaches .

Move the term outside of the limit because it is constant with respect to .

Evaluate the limit of which is constant as approaches .

Evaluate the limit of by plugging in for .

Evaluate the limit of which is constant as approaches .

Simplify the denominator.

Multiply by .

Add and .

Move the negative in front of the fraction.

Rewrite using the commutative property of multiplication.

Multiply .

Multiply and .

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Evaluate limit as h approaches 0 of 1/h*(1/(x+h)-1/x)