What is the derivative of y=e^{x+2ln(x)} ?

The derivative of y=e^{x+2ln(x)} is e^xx^2+2xe^x

What is the first derivative of y=e^{x+2ln(x)} ?

The first derivative of y=e^{x+2ln(x)} is e^xx^2+2xe^x

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derivative of

y = e^{x + 2 l n (x)}

e^{x} x^{2} + 2 x e^{x}

Solution steps

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

Simplify

e^{x + 2 l n (x)} : e^{x} x^{2}

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{x}, g = x^{2}

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

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

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

= e^{x} x^{2} + 2 x e^{x}

3 - 2 x

\frac{cot ^{1} ( s )}{2}

(x^{3})^{\frac{1}{2}}

\frac{sin ( x )}{( sin ( x ) + x ^{2} )}

y = (e^{x})^{2}

What is the derivative of y=e^{x+2ln(x)} ?
The derivative of y=e^{x+2ln(x)} is e^xx^2+2xe^x
What is the first derivative of y=e^{x+2ln(x)} ?
The first derivative of y=e^{x+2ln(x)} is e^xx^2+2xe^x