What is the derivative of (x+1^{e^x}) ?

The derivative of (x+1^{e^x}) is (e^xln(x+1)+(e^x)/(x+1))(x+1)^{e^x}

What is the first derivative of (x+1^{e^x}) ?

The first derivative of (x+1^{e^x}) is (e^xln(x+1)+(e^x)/(x+1))(x+1)^{e^x}

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

(e^{x} ln (x + 1) + \frac{e ^{x}}{x + 1}) (x + 1)^{e^{x}}

Solution steps

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

Apply exponent rule:

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

(x + 1)^{e^{x}} = e^{e^{x} l n (x + 1)}

= \frac{d}{d x} (e^{e^{x} l n (x + 1)})

Apply the chain rule:

e^{e^{x} l n (x + 1)} \frac{d}{d x} (e^{x} ln (x + 1))

= e^{e^{x} l n (x + 1)} \frac{d}{d x} (e^{x} ln (x + 1))

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

= e^{e^{x} l n (x + 1)} (e^{x} ln (x + 1) + \frac{e ^{x}}{x + 1})

e^{e^{x} l n (x + 1)} = (x + 1)^{e^{x}}

= (e^{x} ln (x + 1) + \frac{e ^{x}}{x + 1}) (x + 1)^{e^{x}}

\frac{d}{d x} (cos (x) x^{- 2})

\frac{\partial}{\partial x} (\frac{3 y ^{2}}{x})

\int (3 x^{5} - x^{3} + 6) d x

\int_{0}^{8} \frac{x}{4} d x

x \to - 7 lim (\frac{x + 2}{x})

What is the derivative of (x+1^{e^x}) ?
The derivative of (x+1^{e^x}) is (e^xln(x+1)+(e^x)/(x+1))(x+1)^{e^x}
What is the first derivative of (x+1^{e^x}) ?
The first derivative of (x+1^{e^x}) is (e^xln(x+1)+(e^x)/(x+1))(x+1)^{e^x}