What is the derivative of ln(x^3+e^{2x}) ?

The derivative of ln(x^3+e^{2x}) is 3/x+e^{2x}*2

What is the first derivative of ln(x^3+e^{2x}) ?

The first derivative of ln(x^3+e^{2x}) is 3/x+e^{2x}*2

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\frac{d}{d x} (ln (x^{3}) + e^{2 x})

\frac{3}{x} + e^{2 x} \cdot 2

Solution steps

\frac{d}{d x} (ln (x^{3}) + e^{2 x})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (ln (x^{3})) + \frac{d}{d x} (e^{2 x})

\frac{d}{d x} (ln (x^{3})) = \frac{3}{x}

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

= \frac{3}{x} + e^{2 x} \cdot 2

What is the derivative of ln(x^3+e^{2x}) ?
The derivative of ln(x^3+e^{2x}) is 3/x+e^{2x}*2
What is the first derivative of ln(x^3+e^{2x}) ?
The first derivative of ln(x^3+e^{2x}) is 3/x+e^{2x}*2