Calculus Examples

Find the Derivative - d/dt t/((t-1)^2)
Step 1
Differentiate using the Quotient Rule which states that is where and .
Step 2
Differentiate using the Power Rule.
Tap for more steps...
Step 2.1
Multiply the exponents in .
Tap for more steps...
Step 2.1.1
Apply the power rule and multiply exponents, .
Step 2.1.2
Multiply by .
Step 2.2
Differentiate using the Power Rule which states that is where .
Step 2.3
Multiply by .
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
Simplify with factoring out.
Tap for more steps...
Step 4.1
Multiply by .
Step 4.2
Factor out of .
Tap for more steps...
Step 4.2.1
Factor out of .
Step 4.2.2
Factor out of .
Step 4.2.3
Factor out of .
Step 5
Cancel the common factors.
Tap for more steps...
Step 5.1
Factor out of .
Step 5.2
Cancel the common factor.
Step 5.3
Rewrite the expression.
Step 6
By the Sum Rule, the derivative of with respect to is .
Step 7
Differentiate using the Power Rule which states that is where .
Step 8
Since is constant with respect to , the derivative of with respect to is .
Step 9
Simplify by adding terms.
Tap for more steps...
Step 9.1
Add and .
Step 9.2
Multiply by .
Step 9.3
Subtract from .
Step 10
Simplify.
Tap for more steps...
Step 10.1
Factor out of .
Step 10.2
Rewrite as .
Step 10.3
Factor out of .
Step 10.4
Rewrite as .
Step 10.5
Move the negative in front of the fraction.