Kathy Williams

2022-01-01

what is the derivative of ${\mathrm{sec}}^{2}x$

I'm using the quotient rule and so I rewrite$\mathrm{sec}}^{2}x\text{}\text{as}\text{}\frac{1}{{\mathrm{cos}}^{2}x$

Then set$u=1,u\prime =0\text{}\text{then}\text{}v={\mathrm{cos}}^{2}x$ and $v\prime =-2\mathrm{sin}x\mathrm{cos}x$

I then get$\frac{2\mathrm{sin}x\mathrm{cos}x}{{\mathrm{cos}}^{4}x}$

but when I simplify that I don't get$2{\mathrm{sec}}^{2}x\mathrm{tan}x$ which is the correct answer?

I'm using the quotient rule and so I rewrite

Then set

I then get

but when I simplify that I don't get

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