DIFFERENTIATION

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Find the derivatives

 $y=x^6$ 

•  $\frac{dy}{dx}=6x^5$ 

•  $\frac{dy}{dx}=x^5$ 

Find the derivative

 $y=\frac{1}{\sqrt[3]{x}}$ 

•  $\frac{dy}{dx}=\frac{1}{3x^{\frac{4}{3}}}$ 

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

Find the derivative

 $y=\frac{2}{3}x^5-x^3+5$ 

•  $\frac{dy}{dx}=2x^3-10x+5$ 

•  $\frac{dy}{dx}=\frac{10}{3}x^4-3x^2+5$ 

•  $\frac{dy}{dx}=\frac{10}{3}x^4-3x^2$ 

Find the derivative

 $y=x\left(x^3+2x^{-4}\right)$ 

•  $\frac{\text{d}x}{\text{d}y}=4x^3-10x^{-6}$ 

•  $\frac{\text{d}x}{\text{d}y}=4x^3+10x^{-6}$ 

•  $\frac{\text{d}x}{\text{d}y}=4x^3-6x^{-4}$ 

•  $\frac{\text{d}x}{\text{d}y}=4x^3+6x^{-4}$ 

Find the derivative

 $y=\frac{x^2+3x-3}{x^2}$ 

•  $\frac{\text{d}x}{\text{d}y}=\frac{3}{x^2}+\frac{6}{x^3}$ 

•  $\frac{\text{d}x}{\text{d}y}=-\frac{3}{x^2}+\frac{6}{x^3}$ 

•  $\frac{\text{d}x}{\text{d}y}=-\frac{3}{x^2}-\frac{6}{x^3}$ 

•  $\frac{\text{d}x}{\text{d}y}=-\frac{3}{x^2}+\frac{6}{x^3}$ 

Find the derivative

 $y=\left(2x+3\right)^6$ 

•  $\frac{\text{d}x}{\text{d}y}=12\left(2x+3\right)^5$ 

•  $\frac{\text{d}x}{\text{d}y}=6\left(2x+3\right)^5$ 

•  $\frac{\text{d}x}{\text{d}y}=6x\left(2x+3\right)^5$ 

•  $\frac{\text{d}x}{\text{d}y}=12x\left(2x+3\right)^5$ 

Find the derivative

 $y=\left(12x^3-10\right)^7$ 

•  $\frac{\text{d}x}{\text{d}y}=7\left(12x^3-10\right)^6$ 

•  $\frac{\text{d}x}{\text{d}y}=84\left(12x^3-10\right)^6$ 

•  $\frac{\text{d}x}{\text{d}y}=252x^2\left(12x^3-10\right)^6$ 

•  $\frac{\text{d}x}{\text{d}y}=252x\left(12x^3-10\right)^6$ 

Find the derivative

 $y=\frac{3}{\sqrt[]{x+5}}$ 

•  $\frac{\text{d}x}{\text{d}y}=\frac{3}{2}\left(x+5\right)^{\frac{3}{2}}$ 

•  $\frac{\text{d}x}{\text{d}y}=\frac{-3}{2}\left(x+5\right)^{\frac{3}{2}}$ 

•  $\frac{\text{d}x}{\text{d}y}=\frac{3}{2}\left(x+5\right)^{-\frac{3}{2}}$ 

•  $\frac{\text{d}x}{\text{d}y}=-\frac{3}{2}\left(x+5\right)^{-\frac{3}{2}}$ 

Find the derivative

 $y=\sqrt[5]{x^3-4}$ 

•  $\frac{\text{d}x}{\text{d}y}=\frac{1}{5}\left(x^3-4\right)^{\frac{4}{5}}$ 

•  $\frac{\text{d}x}{\text{d}y}=\frac{3}{5}x^2\left(x^3-4\right)^{-\frac{4}{5}}$ 

•  $\frac{\text{d}x}{\text{d}y}=\frac{3}{5}x^2\left(x^3-4\right)^{\frac{4}{5}}$ 

•  $\frac{\text{d}x}{\text{d}y}=\frac{3}{5}\left(x^3-4\right)^{-\frac{4}{5}}$