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Find the derivative of $y+y^2$ 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 $y+y^2$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
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$\lim_{h\to0}\left(\frac{y+y^2-\left(y+y^2\right)}{h}\right)$
Learn how to solve integral calculus problems step by step online. Find the derivative of (x^2+4x)^3=y+y^2 using the definition. Find the derivative of y+y^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 y+y^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(y+y^2\right). Simplifying. Zero divided by anything is equal to zero.