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

The derivative of x^{{z}(x}) is x^{{z}(x)}(ln(x) derivative of {z}(x)+({z}(x))/x)

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

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

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

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

Solution steps

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

Apply exponent rule:

a^{b} = e^{b l n (a)}

x^{z (x)} = e^{z (x) l n (x)}

= \frac{d}{d x} (e^{z (x) l n (x)})

Apply the chain rule:

e^{z (x) l n (x)} \frac{d}{d x} (z (x) ln (x))

= e^{z (x) l n (x)} \frac{d}{d x} (z (x) ln (x))

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

= e^{z (x) l n (x)} (ln (x) \frac{d}{d x} (z (x)) + \frac{z ( x )}{x})

e^{z (x) l n (x)} = x^{z (x)}

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

x \to 2 - lim (3 x + 6)

\frac{\partial}{\partial y} (x cos (x y))

\frac{\partial}{\partial y} (x^{2} + x y - 25)

\int 2 y - 1 d y

y^{^{'}} + y = 2 t e^{- t} + t^{2}

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