implicit derivative of (dy)/(dx),y=cos(xy)

Topic

Full pad

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

☐²

x^☐

√☐

^□√☐

□□

log_□

θ

∞

∫

ddx

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

implicit derivative tangent volume laplace fourier

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Steps Examples

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∫ tan⁴(x)sec⁶(x)dx

Solution

tan⁵(x)5 +2tan⁷(x)7 +tan⁹(x)9 +C

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Solution steps

One step at a time

x⁶−y⁹=10xy

Treat y as y(x)

Differentiate both sides: 6x⁵−9y⁸dydx =10(y+xdydx )

Isolate dydx : dydx =−10y−6x⁵9y⁸+10x

dydx =−10y−6x⁵9y⁸+10x

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