Calculus Examples

Evaluate the Derivative at t=.002 V=3.0sin(186t)cos(186t) , t=0.002
,
Step 1
Since is constant with respect to , the derivative of with respect to is .
Step 2
Differentiate using the Product 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
The derivative of with respect to is .
Step 3.3
Replace all occurrences of with .
Step 4
Raise to the power of .
Step 5
Raise to the power of .
Step 6
Use the power rule to combine exponents.
Step 7
Differentiate.
Tap for more steps...
Step 7.1
Add and .
Step 7.2
Since is constant with respect to , the derivative of with respect to is .
Step 7.3
Multiply by .
Step 7.4
Differentiate using the Power Rule which states that is where .
Step 7.5
Multiply by .
Step 8
Differentiate using the chain rule, which states that is where and .
Tap for more steps...
Step 8.1
To apply the Chain Rule, set as .
Step 8.2
The derivative of with respect to is .
Step 8.3
Replace all occurrences of with .
Step 9
Raise to the power of .
Step 10
Raise to the power of .
Step 11
Use the power rule to combine exponents.
Step 12
Add and .
Step 13
Since is constant with respect to , the derivative of with respect to is .
Step 14
Differentiate using the Power Rule which states that is where .
Step 15
Simplify the expression.
Tap for more steps...
Step 15.1
Multiply by .
Step 15.2
Move to the left of .
Step 16
Simplify.
Tap for more steps...
Step 16.1
Apply the distributive property.
Step 16.2
Combine terms.
Tap for more steps...
Step 16.2.1
Multiply by .
Step 16.2.2
Multiply by .
Step 17
Evaluate the derivative at .
Step 18
Simplify.
Tap for more steps...
Step 18.1
Simplify each term.
Tap for more steps...
Step 18.1.1
Multiply by .
Step 18.1.2
Multiply by .
Step 18.1.3
Multiply by .
Step 18.1.4
Multiply by .
Step 18.2
Add and .