Calculus Examples

Find the Derivative - d/dx y=(3x^2-4x+1)(5-6x^2)
Step 1
Differentiate using the Product 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 2.4
Since is constant with respect to , the derivative of with respect to is .
Step 2.5
Differentiate using the Power Rule which states that is where .
Step 2.6
Multiply by .
Step 2.7
By the Sum Rule, the derivative of with respect to is .
Step 2.8
Since is constant with respect to , the derivative of with respect to is .
Step 2.9
Differentiate using the Power Rule which states that is where .
Step 2.10
Multiply by .
Step 2.11
Since is constant with respect to , the derivative of with respect to is .
Step 2.12
Differentiate using the Power Rule which states that is where .
Step 2.13
Multiply by .
Step 2.14
Since is constant with respect to , the derivative of with respect to is .
Step 2.15
Add and .
Step 3
Simplify.
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Step 3.1
Apply the distributive property.
Step 3.2
Apply the distributive property.
Step 3.3
Apply the distributive property.
Step 3.4
Apply the distributive property.
Step 3.5
Combine terms.
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Step 3.5.1
Multiply by .
Step 3.5.2
Raise to the power of .
Step 3.5.3
Use the power rule to combine exponents.
Step 3.5.4
Add and .
Step 3.5.5
Multiply by .
Step 3.5.6
Raise to the power of .
Step 3.5.7
Raise to the power of .
Step 3.5.8
Use the power rule to combine exponents.
Step 3.5.9
Add and .
Step 3.5.10
Multiply by .
Step 3.5.11
Multiply by .
Step 3.5.12
Multiply by .
Step 3.5.13
Raise to the power of .
Step 3.5.14
Use the power rule to combine exponents.
Step 3.5.15
Add and .
Step 3.5.16
Multiply by .
Step 3.5.17
Multiply by .
Step 3.5.18
Add and .
Step 3.5.19
Subtract from .
Step 3.5.20
Add and .