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

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

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

\frac{2 ln ( x + 1 )}{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 ln ( x + 1 )}{x + 1}

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

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