Calculus Examples

Find the Derivative - d/dx y=(2x^5+3)cos(x^2)
Step 1
Differentiate using the Product Rule which states that is where and .
Step 2
Differentiate using the chain rule, which states that is where and .
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Step 2.1
To apply the Chain Rule, set as .
Step 2.2
The derivative of with respect to is .
Step 2.3
Replace all occurrences of with .
Step 3
Differentiate.
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Step 3.1
Differentiate using the Power Rule which states that is where .
Step 3.2
Multiply by .
Step 3.3
By the Sum Rule, the derivative of with respect to is .
Step 3.4
Since is constant with respect to , the derivative of with respect to is .
Step 3.5
Differentiate using the Power Rule which states that is where .
Step 3.6
Multiply by .
Step 3.7
Since is constant with respect to , the derivative of with respect to is .
Step 3.8
Add and .
Step 4
Simplify.
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Step 4.1
Apply the distributive property.
Step 4.2
Combine terms.
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Step 4.2.1
Multiply by .
Step 4.2.2
Raise to the power of .
Step 4.2.3
Use the power rule to combine exponents.
Step 4.2.4
Add and .
Step 4.2.5
Multiply by .
Step 4.3
Reorder terms.