AP (Advanced Placement) Derivatives — practice questions
22 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice AP (Advanced Placement) Derivatives in the app →A student differentiates f(x) = x^5 using the power rule. The derivative is:A cost function is the constant f(x) = 7. Its derivative is:For f(x) = 3x^2, a student pulls the 3 out and differentiates the rest. The derivative is:If f(x) = x^3 + x, then f'(x) equals:A function is written as one function multiplied by another. The rule to reach for is the:A student guesses the derivative of a product is simply the product of the derivatives. Is that right?A function appears as one function divided by another. The rule to use is the:A student meets a composition, with one function sitting inside another. The rule for that is the:Differentiating f(x) = (2x + 1)^3 with the chain rule gives:A physics student needs the derivative of sin x. It is:The same student now needs the derivative of cos x. It is:A function is known to be differentiable at a point. What follows about continuity there?Another function is continuous at a point. Must it also be differentiable there?A student differentiates the derivative one more time. The result is the:Third and fourth derivatives, and those beyond, are known together as:Velocity is the rate of change of position. The rate of change of velocity is:An equation cannot be solved neatly for y, so a student differentiates both sides as they stand. That method iKnowing the derivative of a function, a student can also compute the derivative of its:A student differentiates e^x. The result is:The inverse of the natural exponential function has its own name. It is the:A calculus course opens by going back to secant lines and one other kind of line. That other kind is:Average speed over a whole trip differs from speed at one instant. That second quantity is: