MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation
Problem
The derivative of f(x)=−2x7 is f′(x)=−14x6. Which statement best explains why the resulting coefficient is −14 rather than 14?
(a) Differentiating an odd power reverses the sign of its coefficient, resulting in a positive value.
(b) The exponent 7 is multiplied by the coefficient 2, but the negative sign is ignored, giving 14.
(c) The negative coefficient −2 is a constant multiple; by the Constant Multiple Rule it survives differentiation and multiplies the 7, so the new coefficient is −14.
(d) Under the power rule the exponent is reduced by one, so only the power changes and the coefficient stays −2.