Calculus Examples

Find the Derivative - d/d@VAR f(x)=(x^3+x+4)/(2x)
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.
Tap for more steps...
Step 3.1
By the Sum Rule, the derivative of with respect to is .
Step 3.2
Differentiate using the Power Rule which states that is where .
Step 3.3
Differentiate using the Power Rule which states that is where .
Step 3.4
Since is constant with respect to , the derivative of with respect to is .
Step 3.5
Add and .
Step 3.6
Differentiate using the Power Rule which states that is where .
Step 3.7
Combine fractions.
Tap for more steps...
Step 3.7.1
Multiply by .
Step 3.7.2
Multiply by .
Step 4
Simplify.
Tap for more steps...
Step 4.1
Apply the distributive property.
Step 4.2
Apply the distributive property.
Step 4.3
Simplify the numerator.
Tap for more steps...
Step 4.3.1
Simplify each term.
Tap for more steps...
Step 4.3.1.1
Rewrite using the commutative property of multiplication.
Step 4.3.1.2
Multiply by by adding the exponents.
Tap for more steps...
Step 4.3.1.2.1
Move .
Step 4.3.1.2.2
Multiply by .
Tap for more steps...
Step 4.3.1.2.2.1
Raise to the power of .
Step 4.3.1.2.2.2
Use the power rule to combine exponents.
Step 4.3.1.2.3
Add and .
Step 4.3.1.3
Multiply by .
Step 4.3.1.4
Multiply by .
Step 4.3.2
Combine the opposite terms in .
Tap for more steps...
Step 4.3.2.1
Subtract from .
Step 4.3.2.2
Add and .
Step 4.3.3
Subtract from .
Step 4.4
Cancel the common factor of and .
Tap for more steps...
Step 4.4.1
Factor out of .
Step 4.4.2
Factor out of .
Step 4.4.3
Factor out of .
Step 4.4.4
Cancel the common factors.
Tap for more steps...
Step 4.4.4.1
Factor out of .
Step 4.4.4.2
Cancel the common factor.
Step 4.4.4.3
Rewrite the expression.