What is the derivative of ({z}(x)(x)) ?

The derivative of ({z}(x)(x)) is x derivative of {z}(x)+{z}(x)

What is the first derivative of ({z}(x)(x)) ?

The first derivative of ({z}(x)(x)) is x derivative of {z}(x)+{z}(x)

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

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

Solution steps

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

Apply the Product Rule:

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

f = z (x), g = x

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

\frac{d x}{d x} = 1

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

Simplify

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

(3 a b^{2}) + (2 ab + 6)

(ln (6))^{2} d x

a x^{3} - a y^{3} - b y^{3} + b x^{3}

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

(\frac{2}{3} m - n)^{2}

What is the derivative of ({z}(x)(x)) ?
The derivative of ({z}(x)(x)) is x derivative of {z}(x)+{z}(x)
What is the first derivative of ({z}(x)(x)) ?
The first derivative of ({z}(x)(x)) is x derivative of {z}(x)+{z}(x)