Question

Найти производную функции 2^3-15x^2+24x+3 прошу подробно

Answer 1

F(x)=2x³-15x²+24x+3
f'(x)=(2x³-15x²+24x+3)'=(2x³)'-(15x²)'+(24x)'+3'=2*(x³)'-15*(x²)'+24*(x)'+3'=2*3x²-15*2x+24*1+0=6x²-30x+24

Answer 2

Finding the Derivative of the Function

To find the derivative of the function f(x) = 2x^3 - 15x^2 + 24x + 3, we can use the power rule for differentiation. The power rule states that if we have a term of the form ax^n, then its derivative is anx^(n-1).

Applying the Power Rule

Let's find the derivative of each term in the function:

1. The derivative of 2x^3 is 6x^2. 2. The derivative of -15x^2 is -30x. 3. The derivative of 24x is 24. 4. The derivative of a constant term like 3 is 0.

Combining the Derivatives

Now, we can combine these derivatives to find the derivative of the entire function:

f'(x) = 6x^2 - 30x + 24.

So, the derivative of the function f(x) = 2x^3 - 15x^2 + 24x + 3 is f'(x) = 6x^2 - 30x + 24.