What is (\partial)/(\partial x)(x^{e^x}) ?

The answer to (\partial)/(\partial x)(x^{e^x}) is x^{e^x}(e^xln(x)+(e^x)/x)

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(\partial)/(\partial x)(x^{e^x})

\frac{\partial}{\partial x} (x^{e^{x}})

x^{e^{x}} (e^{x} ln (x) + \frac{e ^{x}}{x})

Solution steps

\frac{\partial}{\partial x} (x^{e^{x}})

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (e^{x} ln (x)) = e^{x} ln (x) + \frac{e ^{x}}{x}

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

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

= x^{e^{x}} (e^{x} ln (x) + \frac{e ^{x}}{x})

(- 4) (12.2)

\frac{\partial}{\partial x} ((x^{9}) (y^{6}) + 7 (x^{5}) y)

\int \frac{2 x ^{2} - 4 x + 4}{3 + 2 x - x ^{2}} d x

y^{^{'}} = y - y^{2}

\frac{d y}{d x} = 10 - y

What is (\partial)/(\partial x)(x^{e^x}) ?
The answer to (\partial)/(\partial x)(x^{e^x}) is x^{e^x}(e^xln(x)+(e^x)/x)