Calculus Examples

Find the Derivative - d/dx y=4^(e^(x^2))
Step 1
Differentiate using the chain rule, which states that is where and .
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Step 1.1
To apply the Chain Rule, set as .
Step 1.2
Differentiate using the Exponential Rule which states that is where =.
Step 1.3
Replace all occurrences of with .
Step 2
Differentiate using the chain rule, which states that is where and .
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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 Power Rule.
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Step 3.1
Differentiate using the Power Rule which states that is where .
Step 3.2
Simplify the expression.
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Step 3.2.1
Rewrite as .
Step 3.2.2
Apply the power rule and multiply exponents, .
Step 4
Use the power rule to combine exponents.
Step 5
Simplify.
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Step 5.1
Reorder the factors of .
Step 5.2
Reorder factors in .