Calculus Examples

Find the Derivative - d/dx y=(2e^x)/(x^2+1)
Step 1
Since is constant with respect to , the derivative of with respect to is .
Step 2
Differentiate using the Quotient Rule which states that is where and .
Step 3
Differentiate using the Exponential Rule which states that is where =.
Step 4
Differentiate.
Tap for more steps...
Step 4.1
By the Sum Rule, the derivative of with respect to is .
Step 4.2
Differentiate using the Power Rule which states that is where .
Step 4.3
Since is constant with respect to , the derivative of with respect to is .
Step 4.4
Combine fractions.
Tap for more steps...
Step 4.4.1
Add and .
Step 4.4.2
Multiply by .
Step 4.4.3
Combine and .
Step 5
Simplify.
Tap for more steps...
Step 5.1
Apply the distributive property.
Step 5.2
Apply the distributive property.
Step 5.3
Simplify the numerator.
Tap for more steps...
Step 5.3.1
Simplify each term.
Tap for more steps...
Step 5.3.1.1
Multiply by .
Step 5.3.1.2
Multiply by .
Step 5.3.2
Reorder factors in .
Step 5.4
Reorder terms.
Step 5.5
Simplify the numerator.
Tap for more steps...
Step 5.5.1
Factor out of .
Tap for more steps...
Step 5.5.1.1
Factor out of .
Step 5.5.1.2
Factor out of .
Step 5.5.1.3
Factor out of .
Step 5.5.1.4
Factor out of .
Step 5.5.1.5
Factor out of .
Step 5.5.2
Factor using the perfect square rule.
Tap for more steps...
Step 5.5.2.1
Rewrite as .
Step 5.5.2.2
Check that the middle term is two times the product of the numbers being squared in the first term and third term.
Step 5.5.2.3
Rewrite the polynomial.
Step 5.5.2.4
Factor using the perfect square trinomial rule , where and .