What is the derivative of (z(x^2+z^2)) ?

The derivative of (z(x^2+z^2)) is x^2(dz)/(dx)+2xz+3z^2(dz)/(dx)

What is the first derivative of (z(x^2+z^2)) ?

The first derivative of (z(x^2+z^2)) is x^2(dz)/(dx)+2xz+3z^2(dz)/(dx)

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

x^{2} \frac{d z}{d x} + 2 x z + 3 z^{2} \frac{d z}{d x}

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = z, g = x^{2} + z^{2}

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

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

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

Simplify

\frac{d z}{d x} (x^{2} + z^{2}) + (2 x + 2 z \frac{d z}{d x}) z : x^{2} \frac{d z}{d x} + 2 x z + 3 z^{2} \frac{d z}{d x}

= x^{2} \frac{d z}{d x} + 2 x z + 3 z^{2} \frac{d z}{d x}

(3 x + 4 y = - 2) 5

(x^{2} - 1) y + y^{2} (x + 1) y^{'} (x)

3 (8 π - \frac{64 π - 48 3}{9})

- \frac{K}{x ( x - K )}

1 - cos^{2} (x)

What is the derivative of (z(x^2+z^2)) ?
The derivative of (z(x^2+z^2)) is x^2(dz)/(dx)+2xz+3z^2(dz)/(dx)
What is the first derivative of (z(x^2+z^2)) ?
The first derivative of (z(x^2+z^2)) is x^2(dz)/(dx)+2xz+3z^2(dz)/(dx)