Quotient and Reverse Quotient Rule

QUOTIENT RULE $$R\left(x\right)=\frac{\sin x}{\sec x}$$

$$RW$$ $$R'\left(x\right)=\frac{HO\ d\ HI-HI\ d\ HO\ }{\left[HO\right]^2}$$

$$HO\ \rightarrow$$ ​ ​ (a)   $$HI\ \rightarrow$$ ​ ​ ​ (b)  

$$d\ HO\ \rightarrow$$ ​ (c)   $$d\ HI\ \rightarrow$$ ​ (d)  

$$\left[HO\right]^2\ \rightarrow$$ ​ (e)  

QUOTIENT RULE

$$R\left(x\right)=\frac{13x-5}{16x+3}$$

$$DIF\ \ R'\left(x\right)=$$ RULE

$$ALG\ \ \ R'\left(x\right)=$$ EXP1

$$SIM\ \ \ R'\left(x\right)=$$ EXP2

Submit RULE

QUOTIENT RULE

$$R\left(x\right)=\frac{13x-5}{16x+3}$$

$$DIF\ \ R'\left(x\right)=$$ RULE

$$ALG\ \ \ R'\left(x\right)=$$ EXP1

$$SIM\ \ \ R'\left(x\right)=$$ EXP2

Submit EXP1

QUOTIENT RULE

$$R\left(x\right)=\frac{13x-5}{16x+3}$$

$$DIF\ \ R'\left(x\right)=$$ RULE

$$ALG\ \ \ R'\left(x\right)=$$ EXP1

$$SIM\ \ \ R'\left(x\right)=$$ EXP2

Submit EXP2

REVERSE QUOTIENT RULE $$y=\frac{HI}{HO}$$

$$\frac{dy}{dx}=\frac{\left(9x+8\right)\cdot9-\left(9x+2\right)\cdot9}{\left(9x+8\right)^2}$$

$$HI\ \rightarrow$$ ​ (a)   $$HO\ \rightarrow$$ ​ (b)  

REVERSE QUOTIENT RULE $$y=\frac{HI}{HO}$$

$$\frac{dy}{dx}=\frac{\cos x\ \left(-\ \csc^2x\right)-\cot x\ \left(-\ \sin x\right)}{\cos^2x}$$

$$HI\ \rightarrow$$ ​ (a)   $$HO\ \rightarrow$$ ​ (b)