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Find the derivative of $u^2+v^2$ 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 $u^2+v^2$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
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$\lim_{h\to0}\left(\frac{\left(u+h\right)^2+v^2-\left(u^2+v^2\right)}{h}\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of u^2+v^2 using the definition. Find the derivative of u^2+v^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 u^2+v^2. Substituting f(x+h) and f(x) on the limit, we get. Expand the expression \left(u+h\right)^2 using the square of a binomial: (a+b)^2=a^2+2ab+b^2. Multiply the single term -1 by each term of the polynomial \left(u^2+v^2\right). Simplifying.