Derivatives

Higher-Order Derivatives Review

A higher-order derivative means the derivatives other than the first derivative and are used to model real-life phenomena like most transportation devices such as: Cars. Planes. Rollercoasters​

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​What are higher-order derivatives?

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To find a higher order derivative, you just treat the first derivative as a new function and take its derivative in the ordinary way using derivative rules. Keep taking the derivative either to a specific order or indefinitely.

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​How do I find a higher-order derivative?

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Multiple Choice

Find the given derivative.

• $$x$$  

• $$-2$$  

• $$-2x$$  

• $$0$$  

Multiple Choice

Find the given derivative.

• $$24x$$  

• $$12x^2$$  

• $$12x$$  

• $$24x^2$$  

Multiple Choice

Find the given derivative.

• $$15x^4-2$$  

• $$60x^3$$  

• $$180x^2$$  

• $$0$$  

Multiple Choice

Find the given derivative.

• $$-12+240x^{-6}$$  

• $$-6x^2+12x^{-4}$$  

• $$-12x-48x^{-5}$$  

• $$12-240x^{-5}$$  

Multiple Choice

Find the given derivative.

• $$96x+30$$    

• $$16x^3+15x^2+3$$  

• $$96$$  

• $$48x^2+30x$$   

Multiple Choice

Find the given derivative.

• $$-9x^2+4x-5$$     

• $$-18x+4$$   

• $$-18$$   

• $$0$$    

Multiple Choice

Find $$y^{''}$$  .

• $$4500x^4\left(5x^3+3\right)^5$$     

• $$4500x^2\left(5x^3+3x\right)^3$$   

• $$75x^2\left(5x^3+3\right)^4$$    

•   $$4500x^4\left(5x^3+3\right)^3$$    

Multiple Choice

Find $$y^{''}$$  .

• $$2x^{-\frac{1}{2}}$$      

• $$-x^{-\frac{3}{2}}$$    

• $$\frac{3}{2}x^{-\frac{5}{2}}$$     

•   $$0$$     

Multiple Choice

 If $$f\left(x\right)=3x^3-x+6$$   then find

$$f^{''}\left(2\right)$$  

• $$36$$   

•      $$35$$  

•       $$17$$  

•        $$9$$  

Multiple Choice

What is the 100th derivative of $$y=x^{50}$$  

• $$1$$      

• $$50x$$    

• $$50$$     

•   $$0$$