gradient 3x^2yz+6xy^2z^3

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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

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gradient 3x²yz+6xy²z³

Solution

[

(6yzx+6y²z³)

(3x²z+12xz³y)

(3x²y+18xy²z²)

]

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Solution steps

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Gradient of vector function

For a given vector f(x, y, z) the gradient vector denoted by ∇ (f) is [

∂ ∂ x (f)

∂ ∂ y (f)

∂ ∂ z (f)

]

∂ ∂ x (3x²yz+6xy²z³)

∂ ∂ y (3x²yz+6xy²z³)

∂ ∂ z (3x²yz+6xy²z³)

]

∂ ∂ x (3x²yz+6xy²z³)=6yzx+6y²z³

∂ ∂ y (3x²yz+6xy²z³)=3x²z+12xz³y

∂ ∂ z (3x²yz+6xy²z³)=3x²y+18xy²z²

(6yzx+6y²z³)

(3x²z+12xz³y)

(3x²y+18xy²z²)

]

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−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
▭ \|▭	)	.	0	=	+	`y`

gradient 3x^2yz+6xy^2z^3

Solution

Solution steps

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