Calculus Examples

Find dy/dx y=cos(2x)^x
Step 1
Differentiate both sides of the equation.
Step 2
The derivative of with respect to is .
Step 3
Differentiate the right side of the equation.
Tap for more steps...
Step 3.1
Use the properties of logarithms to simplify the differentiation.
Tap for more steps...
Step 3.1.1
Rewrite as .
Step 3.1.2
Expand by moving outside the logarithm.
Step 3.2
Differentiate using the chain rule, which states that is where and .
Tap for more steps...
Step 3.2.1
To apply the Chain Rule, set as .
Step 3.2.2
Differentiate using the Exponential Rule which states that is where =.
Step 3.2.3
Replace all occurrences of with .
Step 3.3
Differentiate using the Product Rule which states that is where and .
Step 3.4
Differentiate using the chain rule, which states that is where and .
Tap for more steps...
Step 3.4.1
To apply the Chain Rule, set as .
Step 3.4.2
The derivative of with respect to is .
Step 3.4.3
Replace all occurrences of with .
Step 3.5
Convert from to .
Step 3.6
Differentiate using the chain rule, which states that is where and .
Tap for more steps...
Step 3.6.1
To apply the Chain Rule, set as .
Step 3.6.2
The derivative of with respect to is .
Step 3.6.3
Replace all occurrences of with .
Step 3.7
Differentiate.
Tap for more steps...
Step 3.7.1
Since is constant with respect to , the derivative of with respect to is .
Step 3.7.2
Multiply by .
Step 3.7.3
Differentiate using the Power Rule which states that is where .
Step 3.7.4
Multiply by .
Step 3.7.5
Differentiate using the Power Rule which states that is where .
Step 3.7.6
Multiply by .
Step 3.8
Simplify.
Tap for more steps...
Step 3.8.1
Apply the distributive property.
Step 3.8.2
Remove parentheses.
Step 3.8.3
Reorder terms.
Step 4
Reform the equation by setting the left side equal to the right side.
Step 5
Replace with .