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- Find the derivative using the definition
- Find the derivative using the product rule
- Find the derivative using the quotient rule
- Find the derivative using logarithmic differentiation
- Find the derivative
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
- Integrate by parts
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Find the derivative of $7x^3-3x^2+3x-12$ 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 $7x^3-3x^2+3x-12$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
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$\lim_{h\to0}\left(\frac{7\left(x+h\right)^3-3\left(x+h\right)^2+3\left(x+h\right)-12-\left(7x^3-3x^2+3x-12\right)}{h}\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of 7x^3-3x^23x+-12 using the definition. Find the derivative of 7x^3-3x^2+3x-12 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 7x^3-3x^2+3x-12. Substituting f(x+h) and f(x) on the limit, we get. Multiply the single term 3 by each term of the polynomial \left(x+h\right). Multiply the single term -1 by each term of the polynomial \left(7x^3-3x^2+3x-12\right). Add the values -12 and 12.