What is the derivative of ln((x+1^2)-e^{x^2}) ?

The derivative of ln((x+1^2)-e^{x^2}) is 2/(x+1)-e^{x^2}*2x

What is the first derivative of ln((x+1^2)-e^{x^2}) ?

The first derivative of ln((x+1^2)-e^{x^2}) is 2/(x+1)-e^{x^2}*2x

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\frac{d}{d x} (ln ((x + 1)^{2}) - e^{x^{2}})

\frac{2}{x + 1} - e^{x^{2}} \cdot 2 x

Solution steps

\frac{d}{d x} (ln ((x + 1)^{2}) - e^{x^{2}})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (ln ((x + 1)^{2})) - \frac{d}{d x} (e^{x^{2}})

\frac{d}{d x} (ln ((x + 1)^{2})) = \frac{2}{x + 1}

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

= \frac{2}{x + 1} - e^{x^{2}} \cdot 2 x

What is the derivative of ln((x+1^2)-e^{x^2}) ?
The derivative of ln((x+1^2)-e^{x^2}) is 2/(x+1)-e^{x^2}*2x
What is the first derivative of ln((x+1^2)-e^{x^2}) ?
The first derivative of ln((x+1^2)-e^{x^2}) is 2/(x+1)-e^{x^2}*2x