find derivative of f(x)= x⁴/4+x-2?
To find the derivative of the function f(x) = x^4/4 + x – 2, we can use the power rule and the constant rule for differentiation
To find the derivative of the function f(x) = x^4/4 + x – 2, we can use the power rule and the constant rule for differentiation.
According to the power rule, if we have a term x^n, the derivative will be n*x^(n-1). Additionally, the derivative of a constant is zero.
Let’s differentiate each term separately:
1. Differentiating x^4/4:
Using the power rule, we can rewrite x^4/4 as (1/4)*x^4. The 1/4 is a constant, so when we differentiate, it will become zero. The derivative of x^4 is 4x^(4-1) = 4x^3. So, the derivative of x^4/4 is (1/4)*4x^3 = x^3.
2. Differentiating x:
The power rule states that the derivative of x^n is n*x^(n-1). In this case, x is raised to the power of 1, so the derivative of x is 1*x^(1-1) = 1x^0 = 1. However, x^0 equals 1, so the derivative of x is simply 1.
3. Differentiating the constant term (-2):
The derivative of a constant is zero. So, the derivative of -2 is 0.
Now, let’s put all the derivatives together to find the derivative of the entire function f(x) = x^4/4 + x – 2:
f'(x) = x^3 + 1 – 0
= x^3 + 1
Therefore, the derivative of f(x) = x^4/4 + x – 2 is f'(x) = x^3 + 1.
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