Final Answer
Step-by-step Solution
Specify the solving method
Factor the sum or difference of cubes using the formula: $a^3\pm b^3 = (a\pm b)(a^2\mp ab+b^2)$
Learn how to solve problems step by step online.
$derivdef\left(\frac{\left(4a+7\right)\left(16a^{2}-28a+49\right)}{4a+7}\right)$
Learn how to solve problems step by step online. Find the derivative of (64a^3+343)/(4a+7) using the definition. Factor the sum or difference of cubes using the formula: a^3\pm b^3 = (a\pm b)(a^2\mp ab+b^2). Simplify the fraction \frac{\left(4a+7\right)\left(16a^{2}-28a+49\right)}{4a+7} by 4a+7. Find the derivative of 16a^{2}-28a+49 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 16a^{2}-28a+49. Substituting f(x+h) and f(x) on the limit, we get. Multiply the single term -28 by each term of the polynomial \left(a+h\right).