Calculus Examples

Find the Derivative - d/dx x^(sin(x))
Step 1
Use the properties of logarithms to simplify the differentiation.
Tap for more steps...
Step 1.1
Rewrite as .
Step 1.2
Expand by moving outside the logarithm.
Step 2
Differentiate using the chain rule, which states that is where and .
Tap for more steps...
Step 2.1
To apply the Chain Rule, set as .
Step 2.2
Differentiate using the Exponential Rule which states that is where =.
Step 2.3
Replace all occurrences of with .
Step 3
Differentiate using the Product Rule which states that is where and .
Step 4
The derivative of with respect to is .
Step 5
Combine and .
Step 6
The derivative of with respect to is .
Step 7
Simplify.
Tap for more steps...
Step 7.1
Apply the distributive property.
Step 7.2
Combine and .
Step 7.3
Reorder terms.