Calculus Examples

Find the Derivative - d/dx arctan(x/y)
Step 1
Differentiate using the chain rule, which states that is where and .
Step 1.1
To apply the Chain Rule, set as .
Step 1.2
The derivative of with respect to is .
Step 1.3
Replace all occurrences of with .
Step 2
Differentiate.
Step 2.1
Since is constant with respect to , the derivative of with respect to is .
Step 2.2
Multiply by .
Step 2.3
Differentiate using the Power Rule which states that is where .
Step 2.4
Multiply by .
Step 3
Simplify.
Step 3.1
Apply the product rule to .
Step 3.2
Apply the distributive property.
Step 3.3
Combine terms.
Step 3.3.1
Multiply by .
Step 3.3.2
Combine and .
Step 3.3.3
Cancel the common factor of and .
Step 3.3.3.1
Factor out of .
Step 3.3.3.2
Cancel the common factors.
Step 3.3.3.2.1
Factor out of .
Step 3.3.3.2.2
Cancel the common factor.
Step 3.3.3.2.3
Rewrite the expression.
Step 3.4
Simplify the denominator.
Step 3.4.1
To write as a fraction with a common denominator, multiply by .
Step 3.4.2
Combine the numerators over the common denominator.
Step 3.4.3
Multiply by .
Step 3.5
Multiply the numerator by the reciprocal of the denominator.
Step 3.6
Multiply by .