What is the d/(d{x)}(sqrt({x)+{y}+{z}}) ?

The d/(d{x)}(sqrt({x)+{y}+{z}}) is (1+d/(d{x)}({y})+d/(d{x)}({z}))/(2sqrt({x)+{y)+{z}}}

What is the first d/(d{x)}(sqrt({x)+{y}+{z}}) ?

The first d/(d{x)}(sqrt({x)+{y}+{z}}) is (1+d/(d{x)}({y})+d/(d{x)}({z}))/(2sqrt({x)+{y)+{z}}}

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\frac{d}{d x} (x + y + z)

\frac{1 + \frac{d}{d x} ( y ) + \frac{d}{d x} ( z )}{2 x + y + z}

Solution steps

\frac{d}{d x} (x + y + z)

Apply the chain rule:

\frac{1}{2 x + y + z} \frac{d}{d x} (x + y + z)

= \frac{1}{2 x + y + z} \frac{d}{d x} (x + y + z)

\frac{d}{d x} (x + y + z) = 1 + \frac{d}{d x} (y) + \frac{d}{d x} (z)

= \frac{1}{2 x + y + z} (1 + \frac{d}{d x} (y) + \frac{d}{d x} (z))

= \frac{1}{2 x + y + z} (1 + \frac{d}{d x} (y) + \frac{d}{d x} (z))

Simplify

\frac{1}{2 x + y + z} (1 + \frac{d}{d x} (y) + \frac{d}{d x} (z)) : \frac{1 + \frac{d}{d x} ( y ) + \frac{d}{d x} ( z )}{2 x + y + z}

= \frac{1 + \frac{d}{d x} ( y ) + \frac{d}{d x} ( z )}{2 x + y + z}

\int \frac{2 x ^{3} + 6 x ^{2} + 7 x + 4}{x ^{2} + 3 x + 2} d x

y = \frac{1}{x}, (1, 1)

\frac{d}{d x} ((x^{2} + 3 x - 9) e^{x})

\frac{d}{d x} (x^{3} + k y (x)^{2} - 5 x y)

\frac{16 x}{x ^{2} + 16}, at - 2, - \frac{8}{5}

What is the d/(d{x)}(sqrt({x)+{y}+{z}}) ?
The d/(d{x)}(sqrt({x)+{y}+{z}}) is (1+d/(d{x)}({y})+d/(d{x)}({z}))/(2sqrt({x)+{y)+{z}}}
What is the first d/(d{x)}(sqrt({x)+{y}+{z}}) ?
The first d/(d{x)}(sqrt({x)+{y}+{z}}) is (1+d/(d{x)}({y})+d/(d{x)}({z}))/(2sqrt({x)+{y)+{z}}}