What is the derivative of f(x)=e^{ex} ?

The derivative of f(x)=e^{ex} is e^{ex+1}

What is the first derivative of f(x)=e^{ex} ?

The first derivative of f(x)=e^{ex} is e^{ex+1}

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derivative of

f (x) = e^{e x}

e^{e x + 1}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (e x) = e

= e^{e x} e

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

e^{e x} e = e^{e x + 1}

= e^{e x + 1}

y^{^{''}} - 4 y^{^{'}} + 3 y = 0, y (0) = - 4, y^{^{'}} (0) = 5

\frac{\partial}{\partial x} (33 - 3 x^{2} - 3 y^{2})

f (x) = \frac{x}{x ^{2} - 1}, at x = 2

(5 x^{6} + 2 x^{3})^{4}

f (x) = (5 + x) (12 - x) - 2.2 x

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