Question

Which of the following is NOT a correct derivative? a. d/dx cosx = -sinx

b. d/dx(1-x)³ = -3(1-x)²
c. d/dx = (1/x) = -1/x²
d. d/dx(cscx)=-cotx

Answer 1

The option that is NOT a correct derivative is (c) d/dx = (1/x) = -1/x².

Explanation:

The correct derivative of (1/x) is obtained using the power rule for differentiation, which states that the derivative of xⁿ (where n is a constant) is n * x^(n-1). Applying this rule to (1/x) where n = -1, we have:

d/dx (1/x) = -1 * x^(-1 - 1) = -1 * x^(-2) = -1/x²

So, the correct derivative is -1/x². However, option (c) mistakenly equates d/dx to (1/x), which is incorrect.