Question

Найти производную функции y=∜(x^3 )

Answer 1

Y = ∜x³
y = x^(0,75)
y' = 0,75x^(0,75 - 1) = 0,75x^(-0,25)
$y' = \dfrac{3}{4 \sqrt[4]{x} }$

Answer 2

Calculating the Derivative of y = ∜(x^3+)

To find the derivative of the function y = ∜(x^3+), we can use the chain rule. The chain rule states that if we have a composite function, f(g(x)), then the derivative of f(g(x)) with respect to x is given by f'(g(x)) * g'(x).

In this case, our composite function is ∜(x^3+), where the outer function is the fourth root and the inner function is x^3+. Let's break it down step by step:

1. First, let's rewrite the function as y = (x^3+)^1/4. 2. Now, we can apply the chain rule. The derivative of the outer function, (x^3+)^1/4, with respect to the inner function, x^3+, is 1/4 * (x^3+)^(-3/4) * (d/dx)(x^3+). 3. To find the derivative of the inner function, (d/dx)(x^3+), we differentiate x^3+ with respect to x. The derivative of x^3+ is 3x^2. 4. Substituting the derivative of the inner function into the chain rule expression, we have 1/4 * (x^3+)^(-3/4) * 3x^2. 5. Simplifying further, we get the final derivative: dy/dx = 3x^2 / (4 * (x^3+)^3/4).

Please note that the notation x^3+ represents x cubed plus a constant, and the derivative is taken with respect to x.