basic differentiation

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Find the derivative:

 $h\left(x\right)=\frac{4-x^3}{x^2-1}$  

•  $h'\left(x\right)=\frac{\left(x^2-1\right)\left(-3x^2\right)-\left(4-x^3\right)\left(2x\right)}{\left(x^2-1\right)^2}$  

•  $h'\left(x\right)=\frac{\left(4-x^3\right)\left(2x\right)-\left(x^2-1\right)\left(-3x^2\right)}{\left(x^2-1\right)^2}$  

Find the derivative:

 $f\left(x\right)=\frac{3}{5}x$  

•  $f'\left(x\right)=\frac{3}{5}$  

•  $f'\left(x\right)=-\frac{5}{3}x$  

•  $f'\left(x\right)=-3x^5$  

Which of the following is the correct definition of the Power Rule of derivatives?

• Given $f\left(x\right)=x^n$ , $f'\left(x\right)=x^{n-1}$

• Given $f\left(x\right)=x^n$ , $f'\left(x\right)=nx^{n-1}$

• Given $f\left(x\right)=x^n$ , $f'\left(x\right)=\frac{x^{n-1}}{n}$

• Given $f\left(x\right)=x^n$ , $f'\left(x\right)=\frac{n}{x^{n-1}}$

Find the derivative:

 $h\left(x\right)=4\left(2x-11\right)^3$  

•  $h'\left(x\right)=12\left(2x-11\right)^2\left(2\right)$  

•  $h'\left(x\right)=12\left(2x-11\right)^3\left(2\right)$  

•  $h'\left(x\right)=12\left(2\right)^2\left(2x-11\right)$  

Find the derivative for $y=\frac{2x^5+x-4}{x^3}$  

•  $\frac{dy}{dx}=4x^2-\frac{2}{x^2}+\frac{12}{x^3}$  

•  $\frac{dy}{dx}=4x-\frac{2}{x^3}+\frac{12}{x^4}$  

•  $\frac{dy}{dx}=4x^2+\frac{2}{x^3}-\frac{12}{x^4}$  

•  $\frac{dy}{dx}=4x+\frac{1}{2x^3}-\frac{12}{x^4}$  

Find the derivative for $f\left(x\right)=\left(x+2\right)\left(x^2-3\right)$  

•  $f'\left(x\right)=3x^2-3+4x$  

•  $f'\left(x\right)=3x^2-3x+4x-6$  

•  $f'\left(x\right)=3x^2-3+4x-6$  

•  $f'\left(x\right)=x^3-3x+2x^2-6$  

Find the derivative:

 $f\left(x\right)=5x$  

•  $f'\left(x\right)=5$  

•  $f'\left(x\right)=5x$  

•  $f'\left(x\right)=0$