implicit derivative of (dy)/(dx), (x-y)^2=x+y-1

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`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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∫ cos³(x)sin(x)dx

Solution

−cos⁴(x)4 +C

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Solution steps

One step at a time

∫ cos³(x)sin(x)dx

Apply u-substitution: ∫ −u³du

=∫ −u³du

Take the constant out: ∫a·f(x)dx=a·∫f(x)dx

=−∫ u³du

Apply the Power Rule: u⁴4

=−u⁴4

Substitute back u=cos(x)

=−cos⁴(x)4

Add a constant to the solution

=−cos⁴(x)4 +C

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