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When multiplying two powers that have the same base ($x$), you can add the exponents
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$derivdef\left(-96x^2x\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of -96xxx using the definition. When multiplying two powers that have the same base (x), you can add the exponents. When multiplying exponents with same base you can add the exponents: -96x^2x. Find the derivative of -96x^{3} 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 -96x^{3}. Substituting f(x+h) and f(x) on the limit, we get. 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 =.