Calculus Examples

Find the Derivative - d/d@VAR f(x)=4x^2sin(x)tan(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
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
Combine and .
Step 7.5.7
Rewrite in terms of sines and cosines, then cancel the common factors.
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Step 7.5.7.1
Add parentheses.
Step 7.5.7.2
Reorder and .
Step 7.5.7.3
Rewrite in terms of sines and cosines.
Step 7.5.7.4
Cancel the common factors.
Step 7.5.8
Rewrite in terms of sines and cosines.
Step 7.5.9
Multiply .
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Step 7.5.9.1
Combine and .
Step 7.5.9.2
Combine and .
Step 7.5.9.3
Combine and .
Step 7.5.9.4
Raise to the power of .
Step 7.5.9.5
Raise to the power of .
Step 7.5.9.6
Use the power rule to combine exponents.
Step 7.5.9.7
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
Factor out of .
Step 7.6.11
Separate fractions.
Step 7.6.12
Convert from to .
Step 7.6.13
Divide by .
Step 7.7
Reorder factors in .