Do you mean y = (1/2)x4 - (3/2)x2 - x?r-soy said:Q Find all older derivatives
y = X^4/2 = 3/2X^2 -X
What is y4 supposed to be? Since you have taken the derivative, this should be y'. Of the three terms you differentiated on the right side, only one is correct: d/dx[-(3/2)x2] = -3x. The other two terms have errors.r-soy said:y4 = 2X^2 - 3 x ^ 1 - 0
?r-soy said:y4 = 4X^1 - 3 -0
?r-soy said:y4 = 7
"X^0 - 3Find Older Derivatives of y" is a mathematical expression that represents the derivative of y with respect to x, where x is raised to the power of 0 and subtracted by 3. This is also known as the first derivative of y.
To find the older derivatives of y, we can use the power rule of differentiation. This rule states that the derivative of a variable raised to a power is equal to the power multiplied by the variable raised to one less power. In this case, the older derivative of y would be 0 multiplied by x^(-1), which simplifies to 0. Therefore, the older derivatives of y in "X^0 - 3Find Older Derivatives of y" are all equal to 0.
Finding older derivatives of y helps us understand the rate of change of a function. The first derivative (older derivative) of a function represents the slope of the tangent line at a given point on the function's graph. This can be useful in analyzing the behavior of a function and making predictions about its future values.
If we know the older derivatives of y, we can use the process of integration to find the original function. Integration is the inverse operation of differentiation, and it allows us to find the function that would produce the given derivatives. However, it is important to note that there may be multiple functions that have the same derivatives, so additional information or initial conditions may be needed to determine the exact original function.
In this specific expression, the older derivatives of y are all equal to 0. However, in general, older derivatives of y can be negative. This would indicate that the function is decreasing at that particular point. The sign of the older derivatives can give us information about the behavior of the function and its concavity (whether it is curving upwards or downwards).