First Derivative

 $\frac{d}{dx}\left(5x^3\right)$ = 

•  $16x^2$  

•  $15x^3$  

•  $15x^2$  

•  $17x^2$  

 $Find\ the\ f'\left(x\right)\ of\ f\left(x\right)=7x^4$  

•  $28x^3$  

•  $28x^2$  

•  $18x^2$  

•  $18x^3$  

What is three notations used to indicate the first derivative of a function  $y=ax^{n\ }$  

•  $\frac{\text{d}y}{\text{d}x}$  

•  $\frac{a}{x}$  

•  $f'\left(x\right)$  

•  $\frac{\text{d}}{\text{d}x}$  

•  $\log_xy$  

Which one is the graph for  $f\left(x\right)=\ x^2$  

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Based on algebraic function, solve this equation  $\frac{\text{d}}{\text{d}x}\left[5x^3+\frac{3}{4}x^4\right]$  

•  $15x^2+5x^3$  

•  $16x^2+9x^3$  

•  $15x^2+3x^3$  

•  $25x^2+4x^3$  

• Chain Rule

• Product Rule

• Difference Rule

• Power Rule

What will we consider the function if the equation is too difficult to expand, for example  $(𝟐𝒙+𝟑)^4$  

• Algebraic Function

• Composite Function

• Product Function

• Quotient Function

What is the RULE that we use to solve this equation,  $(x^2+1)\left(\sqrt{x-4}\right)$