Which statement best explains why the derivative of equals ?
MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation
Problem
Which statement best explains why the derivative of h(x)=5x3−2x equals h′(x)=15x2−2?
(a) Because h(x) is viewed as the composition 5u3−2u with u=x, so the chain rule gives h′(x)=(15u2−2)⋅1.
(b) Because the derivative of a sum equals the sum of the derivatives, and constant factors multiply the derivative of each term.
(c) Because each term should be treated as a product, such as 5⋅x3 and −2⋅x, so using the product rule yields the result.
(d) Because constants disappear when differentiating, leaving only the variable parts, so the derivative is 15x2−2.