How do you differentiate #f(x)=5x^4-3x^2+2#?

Question

Emilia Aguilar · Accepted Answer

Use three properties of derivatives: The derivative of a sum (or difference) is the sum (or difference) of the derivatives.
This tells us that we can find the derivatives of each term seperately and add(subtract) the derivatives. The derivative of a constant time a function is the constant times the derivative.
This tells us that the coefficients will simply multiply the derivatives of the variable factors. The power rule tells us the the derivative of #x^n# is #nx^(n-1)#.
(You con include the derivative of a constant is #0#.) So: #f(x) = 5x^4-3x^2+2#. #f'(x) = 5(4x^3) - 3(2x^1) + 2(0)#.
So, #f'(x) = 20x^3 - 6x#.

Axel Alvarez · Answer

undefined To differentiate the function f(x) = 5x^4 - 3x^2 + 2, you would apply the power rule of differentiation.

The power rule states that if you have a function in the form f(x) = ax^n, where 'a' is a constant and 'n' is any real number, then the derivative of f(x) with respect to x is f'(x) = n * ax^(n-1).

Using the power rule, you would differentiate each term of the function separately.

The derivative of 5x^4 is 20x^3.
The derivative of -3x^2 is -6x.
The derivative of the constant term 2 is 0.

So, the derivative of the function f(x) = 5x^4 - 3x^2 + 2 is f'(x) = 20x^3 - 6x.