Calculus Examples

Find the Derivative - d/d@VAR f(x)=((2x-5)^7)/(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 using the chain rule, which states that is where and .
Tap for more steps...
Step 3.1
To apply the Chain Rule, set as .
Step 3.2
Differentiate using the Power Rule which states that is where .
Step 3.3
Replace all occurrences of with .
Step 4
Differentiate.
Tap for more steps...
Step 4.1
By the Sum Rule, the derivative of with respect to is .
Step 4.2
Since is constant with respect to , the derivative of with respect to is .
Step 4.3
Differentiate using the Power Rule which states that is where .
Step 4.4
Multiply by .
Step 4.5
Since is constant with respect to , the derivative of with respect to is .
Step 4.6
Simplify the expression.
Tap for more steps...
Step 4.6.1
Add and .
Step 4.6.2
Multiply by .
Step 4.7
Differentiate using the Power Rule which states that is where .
Step 4.8
Combine fractions.
Tap for more steps...
Step 4.8.1
Multiply by .
Step 4.8.2
Multiply by .
Step 5
Simplify the numerator.
Tap for more steps...
Step 5.1
Factor out of .
Tap for more steps...
Step 5.1.1
Factor out of .
Step 5.1.2
Factor out of .
Step 5.1.3
Factor out of .
Step 5.2
Move to the left of .
Step 5.3
Apply the distributive property.
Step 5.4
Multiply by .
Step 5.5
Multiply by .
Step 5.6
Subtract from .