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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

f = x, g = z (x)

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

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

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

Simplify

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

\int (x^{1.9} + 9 x^{3.5}) d x

\frac{d}{d x} (\frac{x}{x ^{- 1} + 4})

\frac{d}{d x} (1 + 2 e^{x})

f (x) = e^{x^{4}}

\frac{\partial}{\partial x} (\frac{1}{x + y + z})

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