Final Answer:
dxd (f(2x 4 ))=9x 3 f ′ (x)=18x2
Step-by-step explanation:
The given equation is a derivative equation which states that the derivative of f(2x 4 ) is equal to 9x 3 . To solve this equation, we need to use the chain rule method. The chain rule states that the derivative of a composite function is equal to the product of derivatives of the inner and outer functions.
In this case, we can express the composite function as f(2x 4 ) which is the product of two functions: 2x 4 and f(x). We can thus calculate the derivative of the composite function by multiplying the derivative of the outer function by the derivative of the inner function.
The derivative of the inner function f(x) is equal to f′(x). The derivative of the outer function 2x 4 is equal to 8x 3 . The product of these two derivatives is equal to 8x 3 *f′(x) = 8x 3 f′(x).
Therefore, the derivative of f(2x 4 ) is equal to 8x 3 f′(x) = 9x 3 f′(x). This equation can now be solved for f′(x) which gives us the result that f′(x) = 18x2. This is the final answer to the given equation.
To recap, the derivative of f(2x 4 ) is equal to 9x 3 f′(x). Solving this equation for f′(x) gives us the result that f′(x) = 18x2.