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`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

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derivative of 1-sec^2(x)

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`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

☐²

x^☐

√☐

^□√☐

□□

log_□

π

θ

∞

∫

ddx

≥	≤	·	÷	`x`^◦	(☐)	\|☐\|	(`f` ◦ `g`)	`f`(`x`)	ln	`e`^☐
(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

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ddx (1−sec²(x))

Solution

−2tan(x)sec²(x)

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Solution steps

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ddx (1−sec²(x))

Simplify 1−sec²(x): −tan²(x)

=ddx (−tan²(x))

Take the constant out: (a·f)′=a·f ′

=−ddx (tan²(x))

Apply the chain rule: 2tan(x)ddx (tan(x))

=2tan(x)ddx (tan(x))

ddx (tan(x))=sec²(x)

=−2tan(x)sec²(x)

Sequences First Term Examples

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