What is the d/(d{x)}(({z})(3sin({z}){x}^2-4{x}+2{y}{z}-{y}^2)) ?

The d/(d{x)}(({z})(3sin({z}){x}^2-4{x}+2{y}{z}-{y}^2)) is {z}(6sin({z}){x}-4)

What is the first d/(d{x)}(({z})(3sin({z}){x}^2-4{x}+2{y}{z}-{y}^2)) ?

The first d/(d{x)}(({z})(3sin({z}){x}^2-4{x}+2{y}{z}-{y}^2)) is {z}(6sin({z}){x}-4)

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\frac{d}{d x} ((z) (3 sin (z) x^{2} - 4 x + 2 y z - y^{2}))

z (6 sin (z) x - 4)

Solution steps

\frac{d}{d x} ((z) (3 sin (z) x^{2} - 4 x + 2 y z - y^{2}))

Take the constant out:

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

= z \frac{d}{d x} (3 sin (z) x^{2} - 4 x + 2 y z - y^{2})

Apply the Sum/Difference Rule:

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

= z (\frac{d}{d x} (3 sin (z) x^{2}) - \frac{d}{d x} (4 x) + \frac{d}{d x} (2 y z) - \frac{d}{d x} (y^{2}))

\frac{d}{d x} (3 sin (z) x^{2}) = 6 x sin (z)

\frac{d}{d x} (4 x) = 4

\frac{d}{d x} (2 y z) = 0

\frac{d}{d x} (y^{2}) = 0

= z (6 x sin (z) - 4 + 0 - 0)

Simplify

= z (6 sin (z) x - 4)

(x^{2} - 4) e^{3 x}

3 (1 - e^{- 0.035 t})

\frac{x ^{3} - 4 x ^{2} + 2 x - 5}{( 2 x - 4 ) ^{2}}

- \frac{6 x ^{2} - 8 x + 3}{( x - 1 ) ^{3}}

(x y^{2} - e^{x^{\frac{1}{3}}}) d x - x^{2} y d y

What is the d/(d{x)}(({z})(3sin({z}){x}^2-4{x}+2{y}{z}-{y}^2)) ?
The d/(d{x)}(({z})(3sin({z}){x}^2-4{x}+2{y}{z}-{y}^2)) is {z}(6sin({z}){x}-4)
What is the first d/(d{x)}(({z})(3sin({z}){x}^2-4{x}+2{y}{z}-{y}^2)) ?
The first d/(d{x)}(({z})(3sin({z}){x}^2-4{x}+2{y}{z}-{y}^2)) is {z}(6sin({z}){x}-4)