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

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

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

The first derivative of {z}(xx) 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)

\int_{0}^{0.1} x arctan (5 x) d x

\int 8 x^{\frac{3}{5}} + 5 x^{- \frac{4}{5}} d x

\frac{d y}{d x} = \frac{( y + 1 )}{x}

\int e^{x} 9 - e^{2 x} d x

\int_{0}^{3} (e^{t} + e^{- t}) d t

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