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

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

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

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

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

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

Solution steps

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

Simplify

(z) (z^{2} x^{2}) : x^{2} z^{3}

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

Apply the Product Rule:

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

f = x^{2}, g = z^{3}

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

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

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

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

x + 16 \cdot x + 1

\frac{29}{73}

20 e^{- 5}

8.61 \cdot 1 0^{- 8}

f^{- 1} [0.2]

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