Question
Differentiate 7x^3-x^-2+1/x
Answers
GPT 3.5
Differentiate the given function 7x^3 - x^(-2) + 1/x with respect to x:
The derivative of 7x^3 is 21x^2 (using the power rule, which states that the derivative of x^n is n*x^(n-1)).
The derivative of -x^(-2) is 2x^(-3) (using the power rule with negative exponents).
The derivative of 1/x is -1/x^2 (using the power rule and the derivative of 1/x is -1/x^2).
Therefore, the differentiated function is:
21x^2 + 2x^(-3) - 1/x^2.
The derivative of 7x^3 is 21x^2 (using the power rule, which states that the derivative of x^n is n*x^(n-1)).
The derivative of -x^(-2) is 2x^(-3) (using the power rule with negative exponents).
The derivative of 1/x is -1/x^2 (using the power rule and the derivative of 1/x is -1/x^2).
Therefore, the differentiated function is:
21x^2 + 2x^(-3) - 1/x^2.