Calculus Examples

Find the Derivative - d/dx arcsin(4x)+arccos(4x)
Step 1
By the Sum Rule, the derivative of with respect to is .
Step 2
Evaluate .
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Step 2.1
Differentiate using the chain rule, which states that is where and .
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Step 2.1.1
To apply the Chain Rule, set as .
Step 2.1.2
The derivative of with respect to is .
Step 2.1.3
Replace all occurrences of with .
Step 2.2
Since is constant with respect to , the derivative of with respect to is .
Step 2.3
Differentiate using the Power Rule which states that is where .
Step 2.4
Factor out of .
Step 2.5
Apply the product rule to .
Step 2.6
Raise to the power of .
Step 2.7
Multiply by .
Step 2.8
Multiply by .
Step 2.9
Combine and .
Step 3
Evaluate .
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Step 3.1
Differentiate using the chain rule, which states that is where and .
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Step 3.1.1
To apply the Chain Rule, set as .
Step 3.1.2
The derivative of with respect to is .
Step 3.1.3
Replace all occurrences of with .
Step 3.2
Since is constant with respect to , the derivative of with respect to is .
Step 3.3
Differentiate using the Power Rule which states that is where .
Step 3.4
Factor out of .
Step 3.5
Apply the product rule to .
Step 3.6
Raise to the power of .
Step 3.7
Multiply by .
Step 3.8
Multiply by .
Step 3.9
Multiply by .
Step 3.10
Combine and .
Step 3.11
Move the negative in front of the fraction.
Step 4
Subtract from .