Differentiate using the Quotient Rule which states that is where and .

Since is constant with respect to , the derivative of with respect to is .

To apply the Chain Rule, set as .

Differentiate using the Power Rule which states that is where .

Replace all occurrences of with .

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.

Add and .

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 .

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.

Add and .

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)