How would you go about finding the derivative of y=1/(3x^2)-5/(2x)?
You can easily rewrite it as
y = 1/3 x^-2 - 5/2 x^-1
then just use the power rule:
y' = 1/3 (-2) x^-3 - 5/2 (-1) x^-2
= -2/x^3 + 5/2x^2
Thank you very much
To find the derivative of the function y = 1/(3x^2) - 5/(2x), we can use the rules of differentiation. The derivative measures the rate of change of a function with respect to its independent variable.
To begin, let's rewrite the function using the power rule for derivatives. The power rule states that if a function is of the form f(x) = x^n, then its derivative is given by f'(x) = n*x^(n-1).
In our case, the function y can be written as:
y = (1/3)x^(-2) - (5/2)x^(-1)
Now, we can differentiate term by term. Let's find the derivative of the first term:
d/dx[(1/3)x^(-2)] = (1/3)(-2)x^(-2-1) = -(2/3)x^(-3)
Similarly, let's find the derivative of the second term:
d/dx[-(5/2)x^(-1)] = -(5/2)(-1)x^(-1-1) = (5/2)x^(-2)
Finally, we can add the two derivatives together to get the derivative of the original function:
y' = -(2/3)x^(-3) + (5/2)x^(-2)
Simplifying further, we can rewrite the derivative as:
y' = -(2/3)/x^3 + (5/2)/x^2
Hence, the derivative of y = 1/(3x^2) - 5/(2x) is y' = -(2/3)/x^3 + (5/2)/x^2.