What is the derivative of (e^x)^2+2ln(x^e) ?

The derivative of (e^x)^2+2ln(x^e) is e^{2x}*2+(2e)/x

What is the first derivative of (e^x)^2+2ln(x^e) ?

The first derivative of (e^x)^2+2ln(x^e) is e^{2x}*2+(2e)/x

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derivative of

(e^{x})^{2} + 2 ln (x^{e})

e^{2 x} \cdot 2 + \frac{2 e}{x}

Solution steps

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

Simplify

(e^{x})^{2} + 2 ln (x^{e}) : e^{2 x} + 2 ln (x^{e})

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (e^{2 x}) = e^{2 x} \cdot 2

\frac{d}{d x} (2 ln (x^{e})) = \frac{2 e}{x}

= e^{2 x} \cdot 2 + \frac{2 e}{x}

\frac{d}{d x} ((x^{3} - 3 x^{2} + 3 x + 1)^{^{'}} - (x - 1)^{^{'}})

(x - 1)^{3} (x + 1)^{2}

6 (x^{2} + 3)^{- 1}

y = x^{2} \cdot (x + 1)^{3}

- 9 sin^{3} (x)

What is the derivative of (e^x)^2+2ln(x^e) ?
The derivative of (e^x)^2+2ln(x^e) is e^{2x}*2+(2e)/x
What is the first derivative of (e^x)^2+2ln(x^e) ?
The first derivative of (e^x)^2+2ln(x^e) is e^{2x}*2+(2e)/x