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Find the derivative of $x^3-5x^2+4$ 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 $x^3-5x^2+4$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
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$\lim_{h\to0}\left(\frac{\left(x+h\right)^3-5\left(x+h\right)^2+4-\left(x^3-5x^2+4\right)}{h}\right)$
Learn how to solve definition of derivative problems step by step online. Factor the expression x^3-5x^2+4. Find the derivative of x^3-5x^2+4 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 x^3-5x^2+4. Substituting f(x+h) and f(x) on the limit, we get. Multiply the single term -1 by each term of the polynomial \left(x^3-5x^2+4\right). Add the values 4 and -4. The cube of a binomial (sum) is equal to the cube of the first term, plus three times the square of the first by the second, plus three times the first by the square of the second, plus the cube of the second term. In other words: (a+b)^3=a^3+3a^2b+3ab^2+b^3 = (x)^3+3(x)^2(h)+3(x)(h)^2+(h)^3 =.