Question

F(x)=1-5x^5 дифференцируйте

Answer 1

Производная равна - 25*х^4 все просто

Answer 2

To differentiate the function $F(x) = 1 - 5x^5$ with respect to $x$, we'll apply the power rule for differentiation. The power rule states that if we have a term of the form $ax^n$, its derivative is $anx^{n-1}$.

So, let's find the derivative of $F(x)$:

$F'(x) = \frac{d}{dx} (1 - 5x^5)$

Apply the power rule to each term:

$F'(x) = \frac{d}{dx}(1) - \frac{d}{dx}(5x^5)$

The derivative of a constant is zero, so the first term becomes zero:

$F'(x) = 0 - 5 \frac{d}{dx}(x^5)$

Now, differentiate $x^5$ using the power rule:

$F'(x) = -5 \cdot 5x^{5-1}$

Simplify:

$F'(x) = -25x^4$

So, the derivative of the function $F(x) = 1 - 5x^5$ with respect to $x$ is $F'(x) = -25x^4$.