You’ll need both the Product and Chain Rules for this one. Therefore this function has no inflection points. Use Quotient Rule to help find the second derivative.Īfter simplification, we find that the second derivative is never equal to 0 and never undefined. Don’t forget to rewrite your radical as a power and use Chain Rule. Of course, you must take the first derivative first. You can find inflection points by taking the second derivative. Problem 3įind all inflection points of the curve defined by. V( t) = x '( t) = cos( cos( 4 t ) ) ( -sin( 4 t ) ) (4)Īt time t = π/8, the velocity is equal to: Be careful - we need two applications of the Chain Rule for this one! Findįind velocity by taking the derivative of the position function. The position of a particle moving along the x-axis at time t is x( t) = sin( cos( 4 t ) ), for 0 ≤ t ≤ π. Then you can find the slope and the equation of the tangent line. Here, we have to use the Power Rule and Sum/Difference Rule. To find a tangent line, first take the derivative. Problem 1įind The tangent line to the curve f( x) = x 4 + 3 x – 10 at the point (1, -6). Now let’s take a look at a few problems involving common derivatives that are modeled after actual AP Calculus problems. Derivatives of inverse trigonometric functionsĬheck out Calculus Review: Derivative Rules and Derivatives on the AP Calculus AB & BC Exams: A Refresher for more. Less common, but no less important are the rules for inverse trig functions. Derivatives of trigonometric, exponential, and logarithmic functions You’ll have to memorize the derivative rules for trig, exponential, and logarithmic functions. That includes: the Power Rule, Product Rule, Quotient Rule, and Chain Rule, among others.ĭon’t forget about those special functions either. But what are the most common derivatives you’ll see on the test? In this short article, we’ll let you in on the secret! Know the Basicsįirst of all, it’s very important to have the basics down. You know you’ll have to know your derivatives inside and out in order to score high on the AP Calculus exam.
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