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Find the derivative of $10b-30ab^2$ 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 $10b-30ab^2$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
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$\lim_{h\to0}\left(\frac{10b-30\left(a+h\right)b^2-\left(10b-30ab^2\right)}{h}\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of 10b-30ab^2 using the definition. Find the derivative of 10b-30ab^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 10b-30ab^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(10b-30ab^2\right). Simplifying. Solve the product -30\left(a+h\right)b^2.