Question

Решите производную функции f(x) =-3x^4 + 5x^3 + 4x ^2 - 2

Answer 1

$f(x)=-3x^4+5x^3+4x^2-1\\f'(x)=-12x^3+15x^2+8x$

Answer 2

To find the derivative of the function $f(x) = -3x^4 + 5x^3 + 4x^2 - 2$, we'll apply the power rule for differentiation. The power rule states that the derivative of $x^n$ is $n \cdot x^{n-1}$.

So, for each term in the function, we differentiate it with respect to $x$ and simplify:

1. $-3x^4$ -> The power rule: $\frac{d}{dx}(-3x^4) = -3 \cdot 4x^{4-1} = -12x^3$

2. $5x^3$ -> The power rule: $\frac{d}{dx}(5x^3) = 5 \cdot 3x^{3-1} = 15x^2$

3. $4x^2$ -> The power rule: $\frac{d}{dx}(4x^2) = 4 \cdot 2x^{2-1} = 8x$

4. $-2$ -> The derivative of a constant is zero: $\frac{d}{dx}(-2) = 0$

Now, putting them all together, the derivative of the function is:

$f'(x) = -12x^3 + 15x^2 + 8x$

So, the derivative of $f(x) = -3x^4 + 5x^3 + 4x^2 - 2$ is $f'(x) = -12x^3 + 15x^2 + 8x$.