Basic Derivatives K12

Which one is your favorite topic in SM015?

• Sequence and Series

• Differentiation

• Matrices

• Polynomials

 $\frac{\text{d}}{\text{d}x}\left(e^2\right)=?$  

• $2x+2\pi$

• $2\pi x+2\pi$

• $2\pi x$

• $2\pi x+\pi^2x$

•  $\pi^2$  

• 0

•  $\pi x$  

•  $\pi$  

Write the correct ANSWERS for  $\frac{\text{d}}{\text{d}t}\left(\pi^3-5e\right)$  

What is anti-derivative?

What is  $\frac{\text{d}}{\text{d}x}\left(\sqrt{x}-\frac{1}{x}\right)=?$  . You can choose more than ONE answer.

•  $\frac{1}{2\sqrt{x}}-\frac{1}{x^2}$  

•  $\frac{1}{2}\sqrt{x}+\frac{1}{x^2}$  

•  $\frac{1}{2\sqrt{x}}+\frac{1}{x^2}$  

•  $\frac{1}{2}x^{-\frac{1}{2}}+\frac{1}{x^2}$  

 $\frac{\text{d}}{\text{d}y}\left(-\frac{1}{y^3}\right)=-3y^{-4}$  is TRUE.

• True

• False

Find the first derivative of the function  $f\left(x\right)=\frac{4}{\sqrt{x+4}}$  

•  $\frac{-2}{\sqrt{x+4}}$  

•  $\frac{2}{\sqrt{x+4}}$  

•  $\frac{2}{\left(x+4\right)^{\frac{3}{2}}}^{ }$  

•  $\frac{-2}{\left(x+4\right)^{\frac{3}{2}}}$  

Given that  $y=3x^7e^{-6}$ , determne  $\frac{\text{d}y}{\text{d}x}$   

•  $-126x^6e^{-7}$  

•  $-126x^6e^{-5}$  

•  $21e^{-6}x^6$  

•  $21x^6e^6$