Final answer to the problem
Step-by-step Solution
Specify the solving method
When multiplying exponents with same base you can add the exponents: $\cos\left(2x\right)^2\cos\left(2x\right)$
Learn how to solve definition of derivative problems step by step online.
$derivdef\left(\cos\left(2x\right)^{3}\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of cos(2x)^2cos(2x) using the definition. When multiplying exponents with same base you can add the exponents: \cos\left(2x\right)^2\cos\left(2x\right). Find the derivative of \cos\left(2x\right)^{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 \cos\left(2x\right)^{3}. Substituting f(x+h) and f(x) on the limit, we get. Factor the sum or difference of cubes using the formula: a^3\pm b^3 = (a\pm b)(a^2\mp ab+b^2). The limit of the product of two functions is equal to the product of the limits of each function.