# Find the Derivative Using Quotient Rule – d/dx (df(x))/(dx)=(d(5x^2-7)^3)/(dx)

Differentiate using the Quotient Rule which states that is where and .
Since is constant with respect to , the derivative of with respect to is .
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 .
Differentiate.
Move to the left of .
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 .
Simplify the expression.
Multiply by .
Reorder the factors of .
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 .
Simplify.
Apply the product rule to .
Simplify the numerator.
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Combine exponents.
Raise to the power of .
Use the power rule to combine exponents.
Subtract from .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Raise to the power of .
Use the power rule to combine exponents.
Subtract from .
Factor out of .
Factor out of .
Factor out of .
Apply the distributive property.
Multiply by .
Multiply by .
Subtract from .
Anything raised to is .
Combine terms.
Multiply by .
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Find the Derivative Using Quotient Rule – d/dx (df(x))/(dx)=(d(5x^2-7)^3)/(dx)