# Find the Derivative f(x)=64/( cube root of 5x^2+7x+8)

Differentiate using the Constant Multiple Rule.
Use to rewrite as .
Since is constant with respect to , the derivative of with respect to is .
Apply basic rules of exponents.
Rewrite as .
Multiply the exponents in .
Apply the power rule and multiply exponents, .
Combine and .
Move the negative in front of the fraction.
Differentiate using the chain rule, which states that is where and .
To apply the Chain Rule, set as .
Differentiate using the Power Rule which states that is where .
Replace all occurrences of with .
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
Subtract from .
Combine fractions.
Move the negative in front of the fraction.
Combine and .
Simplify the expression.
Move to the denominator using the negative exponent rule .
Multiply by .
Combine and .
Move the negative in front of the fraction.
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 .
Simplify the expression.