Calculus Examples

Find the Derivative - d/dx y=(1+sin(x))/(cos(x))
Step 1
Differentiate using the Quotient Rule which states that is where and .
Step 2
Differentiate.
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Step 2.1
By the Sum Rule, the derivative of with respect to is .
Step 2.2
Since is constant with respect to , the derivative of with respect to is .
Step 2.3
Add and .
Step 3
The derivative of with respect to is .
Step 4
Raise to the power of .
Step 5
Raise to the power of .
Step 6
Use the power rule to combine exponents.
Step 7
Add and .
Step 8
The derivative of with respect to is .
Step 9
Multiply.
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Step 9.1
Multiply by .
Step 9.2
Multiply by .
Step 10
Simplify.
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Step 10.1
Apply the distributive property.
Step 10.2
Simplify the numerator.
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Step 10.2.1
Simplify each term.
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Step 10.2.1.1
Multiply by .
Step 10.2.1.2
Multiply .
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Step 10.2.1.2.1
Raise to the power of .
Step 10.2.1.2.2
Raise to the power of .
Step 10.2.1.2.3
Use the power rule to combine exponents.
Step 10.2.1.2.4
Add and .
Step 10.2.2
Move .
Step 10.2.3
Rearrange terms.
Step 10.2.4
Apply pythagorean identity.