DBM 20023 : Basic Rules of Differentiation

Find the derivative for         $f\left(x\right)=2x^5-2x^3+x^2-15$   

•  $10x^4-6x^2+2x$  

•  $10x^4+6x^2-2x$  

•  $10x^4+6x^2+2x$  

•  $10x^4-6x^2-2x$  

Find $\frac{dy}{dx}$  for $y=x^8+2x^6-x^3-4x$  

•  $\frac{dy}{dx}=8x^7-12x^5-3x^2-4x$  

•  $\frac{dy}{dx}=8x^7+12x^5-3x^2-4$  

•  $\frac{dy}{dx}=8x^7+12x^5+3x^2+4x$  

•  $\frac{dy}{dx}=8x^7-12x^5+3x^2+4$  

Find the derivative for $y=\sqrt{x^5}$  

•  $\frac{5}{2}x^{\frac{7}{2}}$  

•  $\frac{5}{2}x^{\frac{1}{2}}$  

•  $\frac{1}{2}x^{\frac{3}{2}}$  

•  $\frac{5}{2}x^{\frac{3}{2}}$  

Tags

CCSS.HSN.RN.A.2

Find the derivative for $y=\sqrt{x}-\frac{1}{3x^2}+10x$  

•  $\frac{dy}{dx}=\frac{1}{2\sqrt{x}}+\frac{2}{3x}+10x$  

•  $\frac{dy}{dx}=\frac{1}{\sqrt{x}}-\frac{2}{3x}+10$  

•  $\frac{dy}{dx}=\frac{1}{2\sqrt{x}}+\frac{2}{3x^3}+10$  

•  $\frac{dy}{dx}=\frac{1}{2\sqrt{x}}-\frac{2}{3x^3}+10$  

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

•  $f'\left(x\right)=3x^2-3+4x$  

•  $f'\left(x\right)=3x^2-3x+4x-6$  

•  $f'\left(x\right)=3x^2-3+4x-6$  

•  $f'\left(x\right)=x^3-3x+2x^2-6$  

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

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 $f\left(x\right)=x^2\left(x^3-2x+5\right)$  

•  $f'\left(x\right)=5x^4+6x^2-10x$  

•  $f'\left(x\right)=5x^4-6x^2-10x$  

•  $f'\left(x\right)=5x^4+6x^2+10x$  

•  $f'\left(x\right)=5x^4-6x^2+10x$  

Find the derivative for $y=\left(1-x^2\right)^5$  

•  $\frac{dy}{dx}=-10x\left(1-x^2\right)^6$  

•  $\frac{dy}{dx}=10x\left(1-x^2\right)^4$  

•  $\frac{dy}{dx}=-10x\left(1-x^2\right)^4$  

•  $\frac{dy}{dx}=10\left(1-x^2\right)^4$  

Find the derivative for $f\left(x\right)=\frac{2}{2x+5}$  

•  $f'\left(x\right)=\frac{-4}{\left(2x+5\right)}$  

•  $f'\left(x\right)=\frac{-4}{\left(2x+5\right)^3}$  

•  $f'\left(x\right)=\frac{4}{\left(2x+5\right)^2}$  

•  $f'\left(x\right)=\frac{-4}{\left(2x+5\right)^2}$  

Find the derivative for $f\left(x\right)=\sqrt{1-2x^2}$  

•  $f'\left(x\right)=\frac{-2x}{\sqrt{1-2x^2}}$  

•  $f'\left(x\right)=\frac{2x}{\sqrt{1-2x^2}}$  

•  $f'\left(x\right)=-2x\sqrt{1-2x^2}$  

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