Calculus Examples

Find dr/dx r=(10+sec(x))sin(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
Differentiate using the Product Rule which states that is where and .
Step 3.2
The derivative of with respect to is .
Step 3.3
Differentiate.
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Step 3.3.1
By the Sum Rule, the derivative of with respect to is .
Step 3.3.2
Since is constant with respect to , the derivative of with respect to is .
Step 3.3.3
Add and .
Step 3.4
The derivative of with respect to is .
Step 3.5
Simplify.
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Step 3.5.1
Apply the distributive property.
Step 3.5.2
Reorder terms.
Step 3.5.3
Simplify each term.
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Step 3.5.3.1
Rewrite in terms of sines and cosines, then cancel the common factors.
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Step 3.5.3.1.1
Reorder and .
Step 3.5.3.1.2
Rewrite in terms of sines and cosines.
Step 3.5.3.1.3
Cancel the common factors.
Step 3.5.3.2
Rewrite in terms of sines and cosines.
Step 3.5.3.3
Combine and .
Step 3.5.3.4
Rewrite in terms of sines and cosines.
Step 3.5.3.5
Multiply .
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Step 3.5.3.5.1
Multiply by .
Step 3.5.3.5.2
Raise to the power of .
Step 3.5.3.5.3
Raise to the power of .
Step 3.5.3.5.4
Use the power rule to combine exponents.
Step 3.5.3.5.5
Add and .
Step 3.5.3.5.6
Raise to the power of .
Step 3.5.3.5.7
Raise to the power of .
Step 3.5.3.5.8
Use the power rule to combine exponents.
Step 3.5.3.5.9
Add and .
Step 3.5.4
Convert from to .
Step 3.5.5
Rearrange terms.
Step 3.5.6
Apply pythagorean identity.
Step 4
Reform the equation by setting the left side equal to the right side.
Step 5
Replace with .