Final answer to the problem
Step-by-step Solution
Specify the solving method
Solve the product $-100y^2\left(5x+104\right)$
Learn how to solve definition of derivative problems step by step online.
$derivdef\left(25x^2+\left(-500x-10400\right)y^2\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of 25x^2-100y^2(5x+104) using the definition. Solve the product -100y^2\left(5x+104\right). Multiply the single term y^2 by each term of the polynomial \left(-500x-10400\right). Find the derivative of 25x^2-500xy^2-10400y^2 using the definition. Apply the definition of the derivative: \displaystyle f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}. The function f(x) is the function we want to differentiate, which is 25x^2-500xy^2-10400y^2. Substituting f(x+h) and f(x) on the limit, we get. Multiply the single term -1 by each term of the polynomial \left(25x^2-500xy^2-10400y^2\right).