Calculus Examples

Find the Derivative - d/dx 6x^2cos(x)cot(x)
Step 1
Since is constant with respect to , the derivative of with respect to is .
Step 2
Differentiate using the Product Rule which states that is where and .
Step 3
The derivative of with respect to is .
Step 4
Differentiate using the Product Rule which states that is where and .
Step 5
The derivative of with respect to is .
Step 6
Differentiate using the Power Rule which states that is where .
Step 7
Simplify.
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Step 7.1
Apply the distributive property.
Step 7.2
Apply the distributive property.
Step 7.3
Combine terms.
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Step 7.3.1
Multiply by .
Step 7.3.2
Multiply by .
Step 7.3.3
Multiply by .
Step 7.4
Reorder terms.
Step 7.5
Simplify each term.
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Step 7.5.1
Rewrite in terms of sines and cosines.
Step 7.5.2
Apply the product rule to .
Step 7.5.3
One to any power is one.
Step 7.5.4
Multiply .
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Step 7.5.4.1
Combine and .
Step 7.5.4.2
Combine and .
Step 7.5.5
Move to the left of .
Step 7.5.6
Move the negative in front of the fraction.
Step 7.5.7
Combine and .
Step 7.5.8
Move to the left of .
Step 7.5.9
Rewrite in terms of sines and cosines, then cancel the common factors.
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Step 7.5.9.1
Add parentheses.
Step 7.5.9.2
Rewrite in terms of sines and cosines.
Step 7.5.9.3
Cancel the common factors.
Step 7.5.10
Rewrite in terms of sines and cosines.
Step 7.5.11
Multiply .
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Step 7.5.11.1
Combine and .
Step 7.5.11.2
Combine and .
Step 7.5.11.3
Combine and .
Step 7.5.11.4
Raise to the power of .
Step 7.5.11.5
Raise to the power of .
Step 7.5.11.6
Use the power rule to combine exponents.
Step 7.5.11.7
Add and .
Step 7.6
Simplify each term.
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Step 7.6.1
Factor out of .
Step 7.6.2
Separate fractions.
Step 7.6.3
Convert from to .
Step 7.6.4
Combine and .
Step 7.6.5
Separate fractions.
Step 7.6.6
Rewrite in terms of sines and cosines.
Step 7.6.7
Rewrite as a product.
Step 7.6.8
Simplify.
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Step 7.6.8.1
Convert from to .
Step 7.6.8.2
Convert from to .
Step 7.6.9
Divide by .
Step 7.6.10
Multiply by .
Step 7.6.11
Factor out of .
Step 7.6.12
Separate fractions.
Step 7.6.13
Convert from to .
Step 7.6.14
Divide by .