Final answer to the problem
Step-by-step Solution
Specify the solving method
Find the derivative of $\left(6x-5y\right)^2$ 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 $\left(6x-5y\right)^2$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
Learn how to solve problems step by step online.
$\lim_{h\to0}\left(\frac{\left(6\left(x+h\right)-5y\right)^2-\left(6x-5y\right)^2}{h}\right)$
Learn how to solve problems step by step online. Find the derivative of (6x-5y)^2 using the definition. Find the derivative of \left(6x-5y\right)^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 \left(6x-5y\right)^2. Substituting f(x+h) and f(x) on the limit, we get. Expand \left(6x-5y\right)^2. The power of a product is equal to the product of it's factors raised to the same power. Multiply the single term 6 by each term of the polynomial \left(x+h\right).