Calculus Examples

Find the Derivative - d/dx y = log base 2 of e^(-x)cos(pix)
Step 1
Differentiate using the chain rule, which states that is where and .
Tap for more steps...
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 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
Differentiate.
Tap for more steps...
Step 4.1
Since is constant with respect to , the derivative of with respect to is .
Step 4.2
Differentiate using the Power Rule which states that is where .
Step 4.3
Multiply by .
Step 5
Differentiate using the chain rule, which states that is where and .
Tap for more steps...
Step 5.1
To apply the Chain Rule, set as .
Step 5.2
Differentiate using the Exponential Rule which states that is where =.
Step 5.3
Replace all occurrences of with .
Step 6
Differentiate.
Tap for more steps...
Step 6.1
Since is constant with respect to , the derivative of with respect to is .
Step 6.2
Differentiate using the Power Rule which states that is where .
Step 6.3
Simplify the expression.
Tap for more steps...
Step 6.3.1
Multiply by .
Step 6.3.2
Move to the left of .
Step 6.3.3
Rewrite as .
Step 7
Simplify.
Tap for more steps...
Step 7.1
Apply the distributive property.
Step 7.2
Combine terms.
Tap for more steps...
Step 7.2.1
Combine and .
Step 7.2.2
Combine and .
Step 7.2.3
Combine and .
Step 7.2.4
Cancel the common factor of .
Tap for more steps...
Step 7.2.4.1
Cancel the common factor.
Step 7.2.4.2
Rewrite the expression.
Step 7.2.5
Combine and .
Step 7.2.6
Combine and .
Step 7.2.7
Cancel the common factor of .
Tap for more steps...
Step 7.2.7.1
Cancel the common factor.
Step 7.2.7.2
Rewrite the expression.
Step 7.2.8
Cancel the common factor of .
Tap for more steps...
Step 7.2.8.1
Cancel the common factor.
Step 7.2.8.2
Rewrite the expression.
Step 7.3
Simplify each term.
Tap for more steps...
Step 7.3.1
Separate fractions.
Step 7.3.2
Convert from to .
Step 7.3.3
Combine and .