# Find the Derivative f(x)=6x^4(9x^2-4x+8) Since is constant with respect to , the derivative of with respect to is .
Differentiate using the Product Rule which states that is where and .
Differentiate.
By the Sum Rule, the derivative of with respect to is .
Since is constant with respect to , the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Multiply by .
Since is constant with respect to , the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Multiply by .
Since is constant with respect to , the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Move to the left of .
Simplify.
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Combine terms.
Multiply by by adding the exponents.
Move .
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Move to the left of .
Multiply by .
Move to the left of .
Multiply by .
Multiply by .
Multiply by by adding the exponents.
Move .
Use the power rule to combine exponents.
Multiply by .
Multiply by .
Multiply by by adding the exponents.
Move .
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Multiply by .
Multiply by .
Multiply by .