P1 Ch12 Polynomial Differentiation

What is the gradient function of  $y=x^3$  

•  $\frac{\text{d}x}{\text{d}y}=3x$  

•  $\frac{\text{d}x}{\text{d}y}=3x^2$  

•  $y=3x^2$  

•  $\frac{\text{d}x}{\text{d}y}=x^2$  

 $f\left(x\right)=7x^4-9+5x^2$  

What is f'(x)?

•  $f'\left(x\right)=28x^3+10x$  

•  $f'\left(x\right)=28x^3-10x$  

•  $f'\left(x\right)=28x^4+10x^2$  

•  $f'\left(x\right)=280x^5$  

 $y=2x^3+7$  

What is the gradient of the curve when x=2?

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 $g=\sqrt{\frac{h^2}{h^5}}$  

Which is equivalent?

•  $g=h^{-\frac{2}{3}}$  

•  $g=h^{-\frac{1}{6}}$  

•  $g=h^{-\frac{3}{2}}$  

•  $g=h^{\frac{3}{2}}$  

Which of the below is true?

• $y+y_1=m\left(x+x_1\right)$

• $y-y_1=m\left(x-x_1\right)$

• $y-y_1=mx+x_1$

• $y=m\left(x-x_1\right)$

 $f\left(x\right)=16\sqrt{x}$   What is the first deruvative of f(x)?

•  $8x^{-\frac{1}{2}}$  

•  $2x^{-\frac{1}{2}}$  

•  $8\sqrt{-x}$  

•  $-8x^{-\frac{1}{2}}$  

 $y=12x^{-2}$   Which of the below is true?

•  $\frac{\text{d}x}{\text{d}y}=-24x^{-1}$  

•  $\frac{\text{d}x}{\text{d}y}=-144x^{-1}$  

•  $\frac{\text{d}x}{\text{d}y}=-24x^{-3}$  

•  $\frac{\text{d}x}{\text{d}y}=24x^{-3}$  

 $f\left(x\right)=3x^4$   What is he value of f ' (2)?

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 $g\left(t\right)=\frac{9}{\sqrt{t^4}}$   Which of the below is correct?

•  $f'\left(x\right)=-\frac{9}{\sqrt{t^5}}$  

•  $f'\left(x\right)=-\frac{32}{t^4}$  

•  $f\ '\left(x\right)=-\frac{18}{t^3}$  

•  $f'\left(x\right)=-\frac{12}{t^5}$  

 $h\left(t\right)=2t^3-10t$  

What is the rate of change when t=3?

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