What is the d/(d{x)}(({z})(3{x}{y}+{z}^2{x}-7{y})) ?

The d/(d{x)}(({z})(3{x}{y}+{z}^2{x}-7{y})) is {z}({z}^2+3{y})

What is the first d/(d{x)}(({z})(3{x}{y}+{z}^2{x}-7{y})) ?

The first d/(d{x)}(({z})(3{x}{y}+{z}^2{x}-7{y})) is {z}({z}^2+3{y})

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\frac{d}{d x} ((z) (3 x y + z^{2} x - 7 y))

z (z^{2} + 3 y)

Solution steps

\frac{d}{d x} ((z) (3 x y + z^{2} x - 7 y))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= z \frac{d}{d x} (3 x y + z^{2} x - 7 y)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= z (\frac{d}{d x} (3 x y) + \frac{d}{d x} (z^{2} x) - \frac{d}{d x} (7 y))

\frac{d}{d x} (3 x y) = 3 y

\frac{d}{d x} (z^{2} x) = z^{2}

\frac{d}{d x} (7 y) = 0

= z (3 y + z^{2} - 0)

Simplify

= z (z^{2} + 3 y)

(3 x + 2) (1 + 1 = 0)

f (x) (ln (x) - x^{2})^{3}

(\frac{1}{x} \circ 7 - x) (x)

\frac{5}{( x + 1 ) ^{2}}

- 2 cos (2 (x - \frac{π}{4})) - 3

What is the d/(d{x)}(({z})(3{x}{y}+{z}^2{x}-7{y})) ?
The d/(d{x)}(({z})(3{x}{y}+{z}^2{x}-7{y})) is {z}({z}^2+3{y})
What is the first d/(d{x)}(({z})(3{x}{y}+{z}^2{x}-7{y})) ?
The first d/(d{x)}(({z})(3{x}{y}+{z}^2{x}-7{y})) is {z}({z}^2+3{y})