Calculus Examples

Find the Derivative - d/dx y=(3(1-sin(x)))/(2cos(x))
Step 1
Since is constant with respect to , the derivative of with respect to is .
Step 2
Differentiate using the Quotient Rule which states that is where and .
Step 3
Differentiate.
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Step 3.1
By the Sum Rule, the derivative of with respect to is .
Step 3.2
Since is constant with respect to , the derivative of with respect to is .
Step 3.3
Add and .
Step 3.4
Since is constant with respect to , the derivative of with respect to is .
Step 4
The derivative of with respect to is .
Step 5
Raise to the power of .
Step 6
Raise to the power of .
Step 7
Use the power rule to combine exponents.
Step 8
Add and .
Step 9
The derivative of with respect to is .
Step 10
Combine fractions.
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Step 10.1
Multiply by .
Step 10.2
Multiply by .
Step 10.3
Multiply by .
Step 11
Simplify.
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Step 11.1
Apply the distributive property.
Step 11.2
Apply the distributive property.
Step 11.3
Simplify the numerator.
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Step 11.3.1
Simplify each term.
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Step 11.3.1.1
Multiply by .
Step 11.3.1.2
Multiply by .
Step 11.3.1.3
Multiply .
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Step 11.3.1.3.1
Raise to the power of .
Step 11.3.1.3.2
Raise to the power of .
Step 11.3.1.3.3
Use the power rule to combine exponents.
Step 11.3.1.3.4
Add and .
Step 11.3.1.4
Multiply by .
Step 11.3.2
Move .
Step 11.3.3
Factor out of .
Step 11.3.4
Factor out of .
Step 11.3.5
Factor out of .
Step 11.3.6
Rearrange terms.
Step 11.3.7
Apply pythagorean identity.
Step 11.3.8
Multiply by .
Step 11.4
Factor out of .
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Step 11.4.1
Factor out of .
Step 11.4.2
Factor out of .
Step 11.5
Rewrite as .
Step 11.6
Factor out of .
Step 11.7
Factor out of .
Step 11.8
Move the negative in front of the fraction.