2.2 Basic Differentiation Rules

Differentiate with respect to x.

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Differentiate with respect to x. $f\left(x\right)=x$  

•  $f'\left(x\right)=1$  

•  $f'\left(x\right)=0$  

•  $f'\left(x\right)=10x$  

•  $f'\left(x\right)=x$  

Differentiate with respect to x. $y=\frac{1}{x^3}$  

•  $\frac{\partial y}{\partial x}=\frac{1}{x^4}$  

•  $\frac{\partial y}{\partial x}=-3x$  

•  $\frac{\partial y}{\partial x}=-\frac{3}{x^3}$  

•  $\frac{\partial y}{\partial x}=-\frac{3}{x^4}$  

Differentiate with respect to x.

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Differentiate with respect to x.

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Differentiate with respect to x.

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Differentiate with respect to x.  $f\left(x\right)=5x^5+\sin x$  

•  $f'\left(x\right)=20x^4+\cos x$  

•  $f'\left(x\right)=25x^4+\cos x$  

•  $f'\left(x\right)=25x^4-\sin x$  

•  $f'\left(x\right)=10x^4+\cos x$  

Differentiate with respect to x.  $f\left(x\right)=4x^{\frac{2}{3}}+\cos x$  

•  $f'\left(x\right)=\frac{8}{3x^{\frac{1}{3}}}+\sin x$  

•  $f'\left(x\right)=\frac{8}{3x^{\frac{1}{3}}}-\sin x$  

•  $f'\left(x\right)=\frac{8}{3}x^{\frac{1}{3}}-\sin x$  

•  $f'\left(x\right)=\frac{6}{x^{\frac{1}{3}}}+\sin x$  

Differentiate with respect to x.  $f\left(x\right)=10x^{10}-\sin x-\cos x$  

•  $f'\left(x\right)=100x^9+\cos x-\sin x$  

•  $f'\left(x\right)=20x^9+\cos x-\sin x$  

•  $f'\left(x\right)=20x^9-\cos x+\sin x$  

•  $f'\left(x\right)=100x^9-\cos x+\sin x$  

Differentiate with respect to x. $f\left(x\right)=\frac{1}{4}x^{\frac{3}{4}}-\cos x+14$  

•  $f'\left(x\right)=\frac{3}{16x^{\frac{1}{4}}}+\sin x$  

•  $f'\left(x\right)=\frac{3}{16x^{\frac{1}{4}}}+\sin x+1$  

•  $f'\left(x\right)=\frac{3x^{\frac{1}{4}}}{16}+\sin x$  

•  $f'\left(x\right)=\frac{3}{16x^{\frac{1}{4}}}-\sin x$