Differentiation — Important Questions

1

Using the power rule: $ \frac{d}{dx}(x^1) = 1x^0 = 1 $.

-1/x²

Since $ \frac{1}{x} = x^{-1} $, using the power rule: $ -1x^{-2} = -\frac{1}{x^2} $.

2x + 3x²

Using sum rule and power rule: $ \frac{d}{dx}(x^2) = 2x $, $ \frac{d}{dx}(x^3) = 3x^2 $, so total is $ 2x + 3x^2 $.

True

This is Newton's Power Formula, which states $ \frac{d}{dx}(x^n) = nx^{n-1} $ for any real number $ n $.