Question

Найдите производную от 5/3x^(3/5) + x^(-4)

Answer 1

Y' = 5/3 * 3/5 *x^(-2/5) -4*x^(-5) = x^(-2/5)-4x^(-5).

Answer 2

Calculating the Derivative

To find the derivative of the function f(x) = 5/3x^(3/5) + x^(-4), we can use the power rule and the sum rule of differentiation.

The power rule states that if we have a function of the form f(x) = ax^n, where a is a constant and n is a real number, then the derivative of f(x) with respect to x is given by f'(x) = anx^(n-1).

Applying the power rule to the first term of the function, 5/3x^(3/5), we get:

f'(x) = (5/3)(3/5)x^((3/5)-1) = x^(-2/5)

For the second term, x^(-4), we can rewrite it as 1/x^4 and apply the power rule:

f'(x) = -4(1/x^(4+1)) = -4/x^5

Therefore, the derivative of the function f(x) = 5/3x^(3/5) + x^(-4) is:

f'(x) = x^(-2/5) - 4/x^5

Please let me know if there's anything else I can help you with!