Calculus Examples

Find dy/dx y=3x^8-sin(x)+x^3tan(x)
Step 1
Differentiate both sides of the equation.
Step 2
The derivative of with respect to is .
Step 3
Differentiate the right side of the equation.
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Step 3.1
By the Sum Rule, the derivative of with respect to is .
Step 3.2
Evaluate .
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Step 3.2.1
Since is constant with respect to , the derivative of with respect to is .
Step 3.2.2
Differentiate using the Power Rule which states that is where .
Step 3.2.3
Multiply by .
Step 3.3
Evaluate .
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Step 3.3.1
Since is constant with respect to , the derivative of with respect to is .
Step 3.3.2
The derivative of with respect to is .
Step 3.4
Evaluate .
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Step 3.4.1
Differentiate using the Product Rule which states that is where and .
Step 3.4.2
The derivative of with respect to is .
Step 3.4.3
Differentiate using the Power Rule which states that is where .
Step 3.5
Simplify.
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Step 3.5.1
Reorder terms.
Step 3.5.2
Simplify each term.
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Step 3.5.2.1
Rewrite in terms of sines and cosines.
Step 3.5.2.2
Apply the product rule to .
Step 3.5.2.3
One to any power is one.
Step 3.5.2.4
Combine and .
Step 3.5.2.5
Rewrite in terms of sines and cosines.
Step 3.5.2.6
Multiply .
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Step 3.5.2.6.1
Combine and .
Step 3.5.2.6.2
Combine and .
Step 3.5.2.7
Move to the left of .
Step 3.5.3
Simplify each term.
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Step 3.5.3.1
Multiply by .
Step 3.5.3.2
Separate fractions.
Step 3.5.3.3
Convert from to .
Step 3.5.3.4
Divide by .
Step 3.5.3.5
Separate fractions.
Step 3.5.3.6
Convert from to .
Step 3.5.3.7
Divide by .
Step 4
Reform the equation by setting the left side equal to the right side.
Step 5
Replace with .